Design and Construction of Physics Demonstration Equipment

DESIGN AND CONSTRUCTION OF PHYSICS DEMONSTRATION EQUIPMENT

Daniel Byrne

DT 260 Industrial and Environmental Physics, DIT Kevin St.

May 2010

2Design and Construction of Physics Demonstration Equipment

ABSTRACT: The goal of this project was to design and construct physics demonstration equipment for the purpose of displaying interesting physics principles to young students and the population in general in order that they may gain a greater understanding and interest in physics, and ultimately attract some to study physics. The fulfillment of this goal was to be the creation of at least three working pieces of demonstration equipment which could be used in front of the public, one capable of producing lissajous figures with laser light and two capable of displaying standing waves both in a gas and on a string. This report details the theory, design and construction of these pieces of equipment, the problems encountered in their design and construction and the results of the undertaking.


ACKNOWLEDGEMENTS:I would like to acknowledgement the following people for the integral part they played in helping me comlete this project.

I would like to thank Joe Keogh for his technical and creative assisstance, for his patience and for his advice. I can safely say that without his help I would have achieved very little in this undertaking. I can also say with complete confidence, that yes, he does have everything! (Well almost)

I would also like to thank Emmet Moore and Hossam Ibrahim for there technical and creative advice throughout the design process and for keeping me motivated with the prospect of the next smoking break.

As well as this I would like to acknowledge and thank Des Hayes, Anne Scully and Alexander 'Sandy' Campbell (I think thats right), for supplying me with some of the components necessary for the project.

Finally I would like to thank the entire DT 260/3 class for being patient enough to listen to me moan, whether they asked how I was getting on or it was spontanious on my part I am most greatful for your ear and for you not biting back, thank you;

Leonard Bolster, Audrey Constancias, Ciara Farrell, Fanny Garcon, Peter Keenan, Michelle McNamara, Emmet Moore, Alan 'God' Murphy, Donal Murphy, Emmet O'Mahony, Hossam Ibrahim and Jerome Vanhooren!

And to anyone who I have neglected to mention I didn't mean to cause offense I'm simply absant minded, just know that I am most greatful to anyone who helped me in anyway complete my project, thank you all.


CONTENTS:

ABSTRACT 2

ACKNOWLEDGMENTS 3

INTRODUCTION 5

CHAPTER 1: THEORY 6

1.1 Oscilloscopes 61.2 Lissajous Figures 81.3 Laser Light 91.4 Laser Health and Safety 101.5 Standing Waves, Nodes, Antinodes & Harmonics 12

CHAPTER 2: STANDING WAVES 14

2.1 Design; Lissajous Figures with Laser Light 142.2 Design; Standing waves in a tube of gas 162.3 Design; Standing waves on a string 17

CHAPTER 3: CONSTRUCTION & RESULTS 19

3.1 Construction of Apparatus; Lissajous Figures with laser light 193.2 Construction of Apparatus; Standing Waves in a tube of gas 22

CHAPTER 4: DISCUSSION & CONCLUSION 25

4.1 Discussion 254.2 Conclusion 26

APPENDIX 27

REFERENCES 29


INTRODUCTION: With only a small percentage of students going on to study science after they’ve completed the leaving certificate each year and even fewer going on to study physics, outreach programs such as those conducted by the School of Physics become increasingly important in attracting young students into the field and more importantly into doing there study at DIT. These outreach programs allow for lecturers and students from the college to speak to young students and display interesting physics principles to them using purpose built pieces of apparatus. The goal of this project was to design and construct some of these apparatus in order that it could be taken out of the college and shown in front of the general public. The first step was to build a piece of apparatus which was capable of generating Lissajous figures using laser light. To do this required a good working knowledge of lasers, including how the functioned, in what ways they could be used for public displays and what were the safety concerns carried with using a laser for public display purposes. This also required knowledge of Lissajous figures and how they could be generated beginning first with an oscilloscope and then working up to generating them using the designed piece of apparatus. Once all of this theory was learnt the next step in the process was to design the piece of apparatus which was to be built and then to actually construct it. After that it was simply a matter of testing the apparatus to ensure it was working correctly and writing an instruction manual for anyone who would be using the apparatus in the future. The next step was to build two pieces of apparatus which were capable of displaying standing waves, one in a tube of gas and the other along a string. This like the piece of apparatus involving the laser meant that good understanding of the principles governing standing waves was required, including an understanding of nodes, antinodes and harmonics. As well as this because one of the pieces involved the use of natural gas or some other combustible gas special safety concerns would have to be made in order to ensure that this was safe for use not just in front of the public but for the person using the piece of apparatus as well. After these safety considerations had been made and all of the theory was understood the process was the same as before, the apparatus needed to be designed, constructed, tested and then an instruction manual was to be written. The project also allowed for the construction of a third piece of apparatus which was not specified. This piece of apparatus was to be picked based on an interesting physics principle which could be developed for display purposes. Once a principle was picked it was to be fully researched and a project brief for it was to be written detailing the aim of the demonstration, the physics theory that was to be illustrated using the demonstration and how the demonstration was to be developed including cost, health and safety concerns and a timeline. Once the brief was complete the apparatus was to be designed, built, tested and demonstrated. After this an instruction manual was to be written. While this project may seem like a group of fairly simple goals its importance cannot be underestimated, the pieces of apparatus to be developed could play a vital role in attracting future students to study at DIT, who will be needed to bolster the number of professionals working in the field of physics in this country.


CHAPTER 1: THEORY

CONTENTS

1.1 Oscilloscopes1.2 Lissajous Figures1.3 Laser Light1.4 Laser Health and Safety1.5 Standing Waves, Nodes, Antinodes & Harmonics

1.1 OSCILLOSCOPES

The Cathode Ray Oscilloscope (CRO) is a device which allows any values of electrical signals, be they voltage, current, power, etc. to be displayed on a screen as function of time. It does this by producing a beam of electrons which are projected onto a glass screen which is coated with phosphor, producing a luminous spot. The electron beam can be deflected up or down and left or right by means of sets of parallel plates which a potential difference across them, this potential difference produces an electric field which can direct the beam accordingly. The movement of the luminous spot in this way produces two-dimensional images on the screen which has x and y axes marked on it. Typically the x-axis deflection is at a constant rate, relative to time, and the y-axis deflection is in response to an input voltage, in this way the CRO can display voltage that changes over times of microseconds and nanoseconds. The main component of the CRO is the cathode ray tube; this produces the electron beam, accelerates it to a high velocity, deflects it to create the image and contains the phosphor coated screen which will display the image. To achieve al this various electrical signals and voltages are required, these can be seen in Figure 1. The cathode ray tube is actually a highly evacuated glass tube which consists of three components; the electron gun, the deflecting system and the display system. The electron gun consists of a cathode and two anodes. The cathode emits electrons by thermionic emission and the quantity of these electrons, which form the beam, is controlled by a grid which is kept at a variable negative potential with respect to the cathode. The purpose of the grid is to control the number of electrons passing it per second, which in turn controls the intensity of the light emitted from the screen. The potential of the grid can be controlled by the INTENSITY control on the Oscilloscope interface. Of the two anodes, the first, the accelerating anode, accelerates the electrons to high speed down the tube while the second, the focusing anode, focuses the beam of electrons to a fine spot on the screen, this can be adjusted by using the FOCUS control on the oscilloscope interface. The deflecting system, mentioned earlier, consists of two pairs of parallel plates which the electron beam passes through. When a potential difference is applied to the Y plates the electric field generated between the plates causes the beam to be deflected in a vertical motion (up and down) depending on the applied potential difference, this is also true for the X plates except this causes the beam to deflected horizontally (from side to side). The display system consists of, as mentioned earlier, a glass screen coated with phosphor. When the high speed electron beam contacts the screen the phosphor molecules absorb the energy from the electrons and reradiate it as visible green light. The CROs in the laboratory are dual beam oscilloscopes, this means that it has two vertical input channels, CH1 and CH2. This allows two different signals to be viewed in tandem as well as independently. As well as being able to display electrical signals as functions of time many CROs are also capable of displaying one electrical as a function of another, it does this by operating in XY mode. If two sinusoidal signals are applied to both the X and Y plates at the same time, then


various patterns will ensue depending upon the frequency, amplitude, and the relative phase difference between the two signals. [1]

FIGURE 1.

To produce a waveform on the screen a signal must first be applied to vertical attenuator (volts/div), this enables the signal to be attenuated. After this the signal is applied to the vertical amplifier, which increases the potential of the input signal to a level that will provide a usable deflection of the beam when applied to the vertical deflecting plates. If the input signal is repetitive e.g. a square wave, the spot must be swept repetitively across the screen to display the signal. This is achieved by the horizontal time base circuit, which generates a sawtooth waveform as shown in Figure 2. This signal is applied to the horizontal amplifier, which increases the amplitude to the level required by the horizontal deflection plates of the cathode ray oscilloscope. As the voltage increases (AB), the beam is caused to traverse the screen from left to right, at a steady speed. When the deflection voltage is reduced to zero (BC), the beam flies back very rapidly to the left hand side of the screen and then starts to move to the right again. The SWEEP TIME/dIV switch controls the speed with which the beam traverses the screen. When the beam and the resultant spot of light

Time/Div

Horizontal Amplifier

Trigger Circuit Time

Delay Line

Vertical Amplifier

Attenuator (Volts/Div)

Input Signal

Time Base Generator

HT Supply

LV Supply

To CTR

To all circuits

Heated Cathode

Intensity Control Grid

Accelerating Anode

Focusing Anode

Vertical Deflection Plates (Y Plates)

Horizontal Deflection Plates (X Plates)

Power Supply Circuit

Fluorescent Screen

Undeflected Beam Path

CRT Glass Envelope

Electron Beam


Linear sweep FlybackB

+

CA

p.d. applied to the X horizontal plates.

0

_

time

traverse the screen sufficiently often, an apparently steady line is displayed on the screen. To synchronize the horizontal deflection with the vertical input, so that the horizontal deflection starts at the same point of the input vertical signal, a synchronizing or triggering circuit is used. This circuit is the link between the vertical input and the horizontal time base.

FIGURE 2.

1.2 LISSAJOUS FIGURES

A Lissajous figure is a pattern that is produced as a result of displaying to sine waves at right angles to one another. This can easily be done on an oscilloscope by putting a waveform from two separate signal generators into each of the channels on an oscilloscope and then setting it to XY mode. The types of patterns which are produced can be controlled by changing the angular frequency of one of or both of the signals being put into the oscilloscope, the amplitude of one of or both of the signals being put into the oscilloscope or by changing the phase difference between the two signals. For instance;

Two sine waves of equal frequency and amplitude, which are in-phase, will producea diagonal to the right.

Whereas two sine waves that are again of equal frequency and amplitude but which are 180 degrees out-of-phase, will producea diagonal to the left.

FIGURE 3A.

FIGURE 3B.

X

Y

X

Y


In order to produce a circle, the two sinewaves again have equal frequency andamplitude but this time they are 90 degreesout-of-phase.

The circle can then be changed to look like aneclipse by adjusting the phase difference to 45 degrees and 135 degrees out-of-phase, producing eclipses to the right and left respectively.

To produce a more complicated shape, suchas a crown, you must begin changing the frequencies, to do this the two sine waves must be in-phase and have the same amplitude,however the of the wave in the x-plane shouldbe twice that of the wave in the y-plane.

For more complicated figures, the ratio between the frequencies and the amplitude should be varied, with the best figures being produced only at specific ratios, as well as this by varying the phase difference between the two waves yet more figures can be achieved. The benefit of the figures produced is that they allow the observer to compare different aspects of the two frequencies being put into the oscilloscope. [2]

1.3 LASER LIGHT

A laser (light amplification by stimulated emission of radiation) is a device which emits a very focused beam of electromagnetic radiation, usually in the visible, however it is also possible to have lasers that operates in the infra-red. For a laser to operate it must abide by a set of very specific conditions. The first of these is a population inversion, there must be more atoms in an excited state than there are at ground state, E2 > E1. To achieve this, the laser must undergo a process known as pumping; this is where a gain material has its electrons brought up to a high energy state by being bombarded with photons. However this presents a problem with two level systems as when the

X

Y

FIGURE 3C.

X

Y

FIGURE 3D.

X

YFIGURE 3E.

Rapid Decay

PumpLaserTransition

Laser beam

L

Gain Material

R1 R2


number of electrons at E2 equals the number of electrons at E1, stimulated emission is likely to occur as a result of the continual bombardment of photons. To avoid this most laser will have at least a three level system so as electron can fall to a middle level before stimulated emission can occur, see Figure 4. The disadvantage of this is that it requires a lot of pump energy. [3]

E E

E2 E2

E1 E1

E0 E0

N N

The second condition which must be met in order for laser light to occur is optical feedback. This means that there must be some means to repeatedly pass the laser beam through the gain material before it is released. This can be achieved simply by placing mirrors at the ends of the chamber which contains the gain material. By using a 50:50 mirror on one end, some of the laser light is allowed to escape and the rest is passed back through the gain material. This set up can be further improved by using curved mirrors which should help to reduce diffraction losses.[3]

The final condition which must be met in order for laser light to occur is there must gains greater than losses. This is difficult as there are only a small amount of gains in the laser so to achieve this, the losses must be kept as low as possible. This means that things such as transmission through the mirror and absorption by the mirror material must be kept as low as possible. As well as things like light scattering in the mirror material and the gain material and diffraction around the mirrors.

1.4 LASER HEALTH AND SAFETY

Due to the power output of lasers they do have the potential to do damage to the human eye and in some cases to skin. For this reason there was a class system developed for lasers which allowed people to be better informed about the risks associated with the particular laser they’re using. This

Before Pumping

Ground State

After Pumping

FIGURE 4.

FIGURE 5.


class system is based on the Maximum Permissible Exposure (MPE). MPE is the highest power or energy density of a light source that can be considered safe, that is the highest power or energy density that has a negligible probability of causing damage. This value is usually about 10% of the value that has a 50% of causing damage under worst case conditions. The MPE is usually calculated at the cornea of the eye or the surface at the skin for each given wavelength and exposure time. The calculation of MPE at the eye is slightly more complicated as the way in which the eye reacts will be different for the different wavelengths, that is to say that different parts of the eye will be more perceptible to some wavelengths than others. Despite this, all calculations of MPE are taken as being the worst case scenario, meaning that it is assumed that the eye lens focuses the laser beam onto the smallest spot possible on the retina for a particular wavelength and that the pupil is fully open. The risk of damage to the eye from laser light is predominately from thermal effects, whereby the eye focuses the light onto a very small area of the retina, which induces a rise in temperature in that vicinity, the reason this is such a threat is that a small rise of even 10 ⁰C can result in the destruction of retinal photoreceptors, with more powerful lasers causing the damage in just a fraction of a second, much faster than the human blink reflex. However damage to the retina will only occur as a result of exposure to wavelengths between 400 nm and 1400 nm as the human eye is not designed to detect wavelengths outside this band, as result of this wavelengths less than 400 nm and greater than 1400 nm will cause damage to the cornea and lens instead. This should be of even more concern when the fact that the blink reflex of the human eye is only designed to respond to visible light and will not react to infra-red or ultra-violet, this means that someone who is being exposed to wavelengths outside of the visible range may not be aware that damage is occurring. For a brief description of possible effects of exposure to various wavelengths see Figure 6.[4]

Wavelength Range Pathological Effects180 – 320 nm (UV-B, UV-C) Photokeratitis (inflammation of the cornea)

320 – 400 nm (UV-A) Photochemical Cataract (clouding of the eye)400 – 780 nm (visible) Photochemical damage to the retina, retinal burn

780 – 1400 nm (near IR) Cataract, retinal burn1.4 – 3.0 μm (IR) Aqueous flare, cataract, corneal burn3.0 μm – 1 mm Corneal burn

FIGURE 6.

There are four classes into which lasers are divided, with the first three each having a subclass. It is important that before any person operates a laser that they are familiar with the class of laser which they are using;

A Class 1 laser is safe under all conditions of normal use; this means that it is not possible for the MPE of this laser to be exceeded.

A Class 1M laser is also consider to be safe under all conditions provided the beam has not

being passed through any optical equipment which may have focused the beam, in which case the class of the laser may have been increased.

A Class 2 laser is consider to be safe but this is only because the human blink will limit the exposure to no more than a quarter of a second, however this class can only be given to lasers which operates in the visible range; 400 – 700 nm.

A Class 2M laser like the 1M is also considered to be safe provided the beam isn’t exposed to any optics which would focus it.


A Class 3R laser can be considered to be safe provided that it is handled carefully, the reason for this is the MPE on it can be exceeded but with only a low risk of injury.

A Class 3B laser unlike the 1M and 2M lasers is to be considered hazardous to the eye if it is exposed directly, for this reason all lasers in this class must be equipped with a key switch and a safety interlock and it is also recommended that protective eyewear is worn while the laser is in use.

Any laser which cannot be classed as a Class 3B laser or below is to be considered a Class 4. These lasers usually carry high risk as they can burn skin and are capable of igniting combustible materials. As well as this diffuse reflections from surfaces in the vicinity of the laser can result in eye damage with direct expose possibly causing permanent damage. As a result of this all Class 4 lasers must be equipped with a key switch and safety interlock and protective eyewear must be worn at all times while the laser is in use.

The reason for the difference between the Classes 1 & 2 and the Classes 1M & 2M respectively is that the M classes have a large diameter which means they can have a higher power output and still be considered to be a Class 1 or 2, but If the beam from a one of the M classes was to be focused then there would be a much more power over a smaller area which increases its class rating. [5]

2.1 STANDING WAVES, NODES, ANTINODES & HARMONICS

A standing wave is one which does not change its position, that is that the peaks and troughs do not move along the length of the medium, but only oscillate up and down. This can happen for one of two reasons, firstly, the medium through which the wave is travelling may be moving in the opposite direction that of the wave. The second reason for this to occur is that there is a second wave with the same frequency, wavelength and amplitude moving in the opposite direction of the wave. Standing waves can be seen in a number of instances, for example, if a string is tied to a fixed point and a wave is sent through it, when the wave reaches the end of the string it will be reflected back onto itself resulting in a standing wave. Another instance would be when two waves in with the same wave period but moving in opposite directions, in the open ocean, a standing wave will be formed. [6]

FIGURE 9.


In a standing wave the node is the point on the wave which has minimal amplitude. This is easily distinguishable as it appears to be the part of the wave which isn’t moving at all, the opposite is true of the antinode, this is the point on the wave which has maxim amplitude and appears to be the most. The nodes can be located at evenly spaced intervals down the length of the medium, with one occurring every half of a wavelength (λ/2) and antinodes occurring halfway between each node. For a clearer view of this see Figure 10. [7]

FIGURE 10.

The number of nodes or antinodes on a string is determined by the harmonic of the wave. The harmonic of the wave is a component of the wave which is an integer of the fundamental frequency, which is to say if the fundamental frequency is f, the first, second and third harmonics will have the frequencies, 1f, 2f and 3f respectively. This is better illustrated in Figure 11. [8]

FIGURE 11.


CHAPTER 2: DESIGN

CONTENTS

2.1 Design; Lissajous Figures with Laser Light2.2 Design; Standing waves in a tube of gas2.3 Design; Standing waves on a string

2.1 DESIGN; LISSAJOUS FIGURES WITH LASER LIGHT

As this was not the first incarnation of the piece of apparatus, there were already well established designs on how to construct it. The most common design was one which incorporated two rotating mirrors which were fixed to the axles of motors, the speeds of which could be controlled, while a laser beam was bounced from one mirror to the other. The important aspect of the design was the mirrors, each was angled slightly with respect to the axle in order to produce a phase difference between them, and then as each mirror rotated it velocity simulated a frequency, which could be changed by changing the speed at which it rotated. As this design seemed relatively simple and easy to achieve compared with others available it was chosen, see Figure 7. The design specified the use of 1.5 – 3 V motors, which would provide adequate power while not being unnecessarily large. These motors could be run off of 1.5 volt size D batteries, one for each motor. The mirrors were to be light plastic so as to reduce the load on the motors and allow them to run more efficiently. This meant yielding some of the quality which comes with using glass mirrors, but these would have been too heavy for the motors to runs efficiently. The only specification for the laser was that it was to be a pen laser, as this was to be more than adequate for the purpose. With this in mind a 3 volt pen laser was chosen being run of the two 1.5 volt batteries which were to be connected in series in order to power it. The design also called for two potentiometers to be wired into the circuit so as the voltage supply to the motor and hence its rotational velocity could be controlled, however different designs called for vastly different size potentiometers ranging in values from 2.2 kΩ to 25 Ω despite the fact that it listed the same type of motor in each design. As this was quite contradictory it was necessary to test the motors being used and find out which resistance would yield the best result, after testing it was determined that two 100 Ω potentiometers would work best. Also required were two toggle switches so as the motors could be run both forward and in reverse and for another toggle switch so as the laser could be switched on and off easily. This was necessary as the laser had a switch built into it that required it to be held down while the laser was working and when it was released the laser would shut off, by introducing a toggle switch to this the switch on the laser could be pinned in the on position leaving the toggle switch to control the laser. [9]


Figure 7 shows a rudimentary layout for the apparatus.

FIGURE 7.

Figure 8 shows the circuit diagram for the apparatus.

FIGURE 8.

M

MLASER

1.5 V

1.5 V

1.5 V

1.5 V

100 Ω

100 Ω

3 V

Motor Switches

Laser Switch

Laser

Batteries

Motor

Potentiometers

Mirrors

Motor

To Signal Generator

Loudspeaker

Rubber/Latex Diaphragm

To Gas

Rubber Bung

Flow ControlValve


2.2 DEISGN; STANDING WAVES IN A TUBE OF GAS

The concept of producing standing waves in a tube of gas is not a new one, it has actually been worked into a physics experiment known as Ruben’s Tube. The experiment involves taking a metal tube which has a number of perforations in a straight line along the entire length of the tube, attaching a gas supply to one end of the tube and a loud speaker to the other, effectively sealing the tube at both ends. The tube is then filled with gas which can only escape through the perforations along its length. When the gas is lit a number of uniform flames can then be observed along the tube, when a signal is put through the loudspeaker via a signal generator a standing wave can be observed in the flames emanating from the tube. The difficult part of the assembly process is mounting the loudspeaker, there are two approaches to this. The first approach calls for the loudspeaker to be mounted directly to the tube with no interface between the two, this means that pressure changes in the gas resulting from the waveform come directly from the speaker, this also means that there is higher risk of gas leakage around where the speaker is mounted, due to the difficult in mounting the speaker with a non flammable sealant. The second approach is to mount a rubber seal between the speaker and the tube, this will provide an airtight seal around the end of the tube and better transmit the sound waves through the tube. The problem with this approach is that the speaker cannot be fixed in place permanently as over the time the rubber seal will wear down and will need to be changed this necessitates that it be easy to remove the loudspeaker from the end of the tube. Beyond the problem with whether the speaker should be mounted directly to the tube the design for the apparatus was fairly simple, it required a metal tube about two meters long, a suitably sized loudspeaker to fit onto the tube, a meter or two of rubber hosing, something to seal the end of the tube which the gas entered through, some wooden supports for the tube, a flow control valve, a signal generator and some rubber or latex to seal the other end of the tube if that option was taken.To see how these fitted together see Figure 12. [10]

FIGURE 12.

Metal Tube

WoodenSupports


2.3 DESIGN; STANDING WAVES ON A STRING

To develop standing waves on a string is a fairly easy thing to do, you simply put the string under tension and apply a signal, however developing a piece of apparatus that is capable of doing this is independently of an operator can be quite difficult, especially when there is the requirement for the apparatus to be both robust and transportable. Most designs require the use of a wave driver which can be large and quite heavy, the other problem with this kind of equipment is that because it is usually designed for use in things such as Melde’s Experiment it often only produces very small standing waves which are of little use for demonstration purposes as they do not provide a significant impact when being viewed by an observer. A loudspeaker could also have been used in the place of a wave driver, which would eliminate the associated weight problems but there is still the issue of the loudspeaker not providing significant enough impact to the observer. As neither the wave driver nor the loudspeaker met the requirements for the apparatus this necessitated the design of new piece of equipment which could provide the same function but without the disadvantages. The solution to the problem was to use a motor to provide the vertical motion in the string, this meant simply designing something that could turn the motors circular motion into linear motion. The first piece of equipment designed to this involved a cogged wheel lifting a grooved bar up and then letting it drop to its starting position, with this process repeating over and over again. The problem theorized with this system however was that after a short amount of time the bar would settle into a natural mode, whereby it would only move up or down a small amount as a groove in it would just continue to rise slightly before dropping onto the next successive gear. See Figure 13. The next design consisted of a similar system but without the cogged wheel or grooved bar. Instead there would be a single grove on the top of the bar and an arm on the axle of the motor which would repeatedly catch it, lifting it up before letting it drop again, with this action repeating over and over again providing a vertical motion. The problem with this however was that if the motor was spinning to fast the bar would never get to fall completely and as in the case of the previous design would get into natural mode whereby it only moved a very small amount. See Figure 14.

FIGURE 13A. FIGURE 13B.

Grooved Bar

Cogged Wheel

Housing

Motor Axlewith bar

Bar with single grove

Housing


The solution to these problems was to drive the string up and down by running it straight off an arm coming from the motor. This worked by attaching the string to the end of an arm which was being driven around by the motor and then having the string pass through a vertical slit in a sheet of perspex which would only allow the string to move in a vertical motion, providing a signal. The harmonic of the wave on the string could then be adjusted by adding or subtracting weights from the end of the string via a pulley. See Figure 14.

FIGURE 14.

While the amplitude of the wave produced from this design was greater than that of the wave driver or loudspeaker, it still wasn’t adequately large that it could be left on a bench and be viewed easily, so it was proposed that it have the ability to be mounted on a whiteboard using magnets. This however was very limiting as not all whiteboards can take magnets, so instead of using magnets it was decided that suction cups could be used, this meant that it could be mounted on any surface provided it was relatively smooth. See Figure 15.

FIGURE 15.

Plastic SheetMotor witharm

Standing Wave Pulley

Weights

Suction Cups

Motor

Perspex SheetStanding Wave

Weights

PulleyWall Mounts


CHAPTER 3: CONSTRUCTION & RESULTS

CONTENTS

3.1 Construction of Apparatus; Lissajous Figures with laser light3.2 Construction of Apparatus; Standing Waves in a tube of gas3.3 Construction of Apparatus; Standing Waves on a string

3.1 CONSTRUCTION OF APPARATUS; LISSAJOUD FIGURES WITH LASER LIGHT

Initially construction began using two unmatched motors which were available in the lab, the maximum rotational velocity of each motor was measure using a tachometer, this is device used to measure the rotational speed, the result of this was that one motor had a rotational velocity significantly greater than the other. To try and over come this more voltage was applied to the slower motor while less voltage was applied to the faster. Initially this resulted in both motor running at approximately the same velocity, however when the velocities were to be adjusted it proved quite difficult to control the ratio of the velocities due to the fact that they were drawing different amount of voltage. As a result of this it was necessary to acquire a set of matching motors from an electronics supply store. When these motors were tested using the tachometer they were found to be running at almost identical velocities while both drawing the same amount of voltage. This made it much easier to control the ratio of velocities when it was time to adjust the speeds of the motors. After the motors were acquired it was necessary to mount the mirrors which had been acquired at an earlier stage. To do this a length of plastic rod was divided in two and cut down to an appropriate length and each length then had a hole drilled into its core using a lathe, this allowed the rod to be mounted directly onto each axle. After the holes were drilled the end of the rod which the mirror was to be mounted on had a slight angle put on it, this was done using a belt sander. The reason for this was to produce a phase difference between the two mirrors when they were mounted on the motors. Before the mirrors were mounted to the motors each was cut in a rough circle using a shears, this was simply done to reduce the weight on the motors axle and to stop the corners of the otherwise square mirrors from catching on anything. Once the mirrors were cut into shape they were mounted onto the plastic rod using and hot glue gun which were in turn mount in turn mounted onto the axle of each motor using superglue. After the two mirror assemblies were finished a 3 V pen laser was acquired from one of the labs. This was stripped of the battery compartment in it as it would be run off the two batteries running the motors. When the battery compartment was removed a wire was wrapped around the spring which was emerging from where the battery compartment had been and a second wire was wrapped around the other terminal. After this was done a small piece of parcel tape was used to keep the switch on the laser in the on position. The entire rear assembly was then covered with a heat shrink sleeve in order to conceal the brown tape and any exposed parts of the assembly. After the laser assembly was complete a number of switches were acquired; a single pole single throw switch would operate the laser and two double pole double throw switches which would allow the motors to be run in forward and reverse. Also acquired at this point were two 100 Ω ten turn potentiometers, which would allow the voltage to the motors and hence their velocity to be controlled. The final component to be acquired were the batteries, these came with a set of holders so as each battery could be replaced as each battery was worn out. The next step was to acquire materials to mount the various components and a base board for the components to be mounted to. This consisted of three wooden blocks with the dimensions 49 x 49 x 12 mm, for the two motor

49 mm

49 mm

49 mm

49 mm

13 mm20 mm

20 mm


assemblies and laser assembly and a base board 400 x 176 x 12 mm. The mount for the motors required that a slot be cut into each block where they would rest, 20 x 20 mm, see Figure 16A. The mount for the laser was much simpler only requiring a hole to be bored through the mounting, 13 mm in diameter, see Figure 16B. As the hole in which the laser sat was quite tight it was no necessary to glue the laser in place, however the motors were quite loose in their mounting so it was necessary to fix them in place using the hot glue gun.

FIGURE 16A. FIGURE 16B.

Once the motor and laser assemblies were fixed in there mountings all of the components could be fixed to the board. This began with drilling holes for the switches and then filling them square so the would fit into place neatly, these however could not be fixed into place until they were wired into the rest of the circuit. The purpose of drilling the holes before hand was to establish were they would reside on the board. The first thing to be fixed to the board were the battery holders, the reason for this being that as they were largest component on the board everything would have to be place fixed around them. Given that the mirrors on the motors were at a slight angle relative to the axles it would not be a simple matter of just facing one toward the other. The reason for this being that as the first mirrors rotated it would direct the laser beam in a wide circle, this meant it was necessary to place the mirror in a location such that it would be struck by the beam at every point in the circle. To do this the laser and first motor assembly was attached by the board using blue tack, this way they could both be adjusted as needed. However before either of these were adjusted the second motor assembly was placed in a number of locations and angles to try and intercept the beam. When the beam could not be intercepted completely then the first motor assembly or the laser could be adjusted accordingly. When the right location was found the base board was marked accordingly and each piece was fixed in place in turn using the hot glue gun. Once the three assemblies and batteries were secured in their places the potentiometers could be fixed in what ever space was left available to them. After everything was finally fixed in place, all of the components could be wired together to form the circuit a complete circuit. To see the exact manner in which this was done please refer to Figure 8 on page 11. As the wiring was being done a heat shrink sleeve was applied at various points in order to keep groups of wire in order and stop them from obstructing any of the components on the board. When the wiring was completely finished the switches were fixed in place using the hot glue gun with the wires emanating from them coming out of the side of the holes. At this point the apparatus was ready to be tested. Beginning first with each motor, being first switched on and run in forward, next in reverse, the potentiometers were used to vary the speed of each motor. Then it was the turn of the laser to be tested, simply a matter of switching it on and off. Once it was established that each component was working efficiently the apparatus was ready to be tested as whole.


Unfortunately this was not a success. When the motors were switch off the laser beam could clearly be seen coming off of the second mirror at good distance. However once even one of the motors was switched on the laser could not be seen at all. The reason for this was unknown and so several theories were developed for the possible reason this could be happening, so these theories were tested independently and then in unison to see if they could solve the problem. The first concern was that due to the face that the mirrors being used were plastic and of poor quality that they were not transmitting the beam. To combat this some high quality front surfaced mirrors were acquired from the optics lab and were fitted in place of the old ones using exactly the same technique. However when the apparatus was tested with these new mirrors exactly the same result was observed, with the exception that the motors weren’t running as smoothly due to extra load contributed by the glass mirrors. As a result of this the glass mirrors were removed and the old ones put back in place. The second concern was that the laser may not be adequately powerful to be reflected off of both mirrors while they were spinning resulting in all of the light being dispersed. To test this theory the 3 V laser being used was removed from its mounting, but not from the circuit, and in its place a 12 – 15 V Class 2 laser was used. This was run off an external power source and was propped in the same place as the old laser, its beam pointing through the hole in the mounting for the old laser. When this was tested the new laser did perform better than the old laser reaching out to about four feet before the beam disappeared, however this shed light on a different problem which had not been seen until this point. When the laser beam came off of the two mirrors it was not producing lissajous figures but rather a figure that looked like a scribble on a piece of paper. At first it was assumed that this was just a result of the frequencies not being in the correct ratio but the image formed did not change to a lissajous at any point as the frequencies were adjusted.This meant that there were now two problems with the apparatus, firstly the strength of the laser and second, the fact that lissajous figures were not being produced. The problem with the laser was still present as it was not simply a matter of replacing the old pen laser with the new more powerful laser. The reason for this being twofold, the actual size of the new laser, in terms of dimensions, was much larger than anything mounted on the board and there was no room left to accommodate it on the board. The second problem with the new laser was the amount of power required to run it, even if the new laser could be mounted to the board, the power requirements would also necessitate the mounting of several more batteries in order for it to function. At that point it would have been unfeasible to attempt to use the new laser with two other pieces of apparatus to be built. However it was possible to address the problem with lissajous figures not being produced.The only possible problem which could be seen with the apparatus not doing as it was meant to at this stage was that the angles which the mirrors were mounted at were to severe and had to be adjusted. To do this the plastic mirrors were removed and the rod on which they were mounted was sanded down to a smaller angle, this was also done with the front surfaced mirrors so as they could also be tested with the hope that they might produce results now despite earlier failures. After all the rods were sanded down the mirrors were fixed back into position using the same procedure as before. The rods with the mirrors were then mounted back onto the axle of the motors and the test could then be performed again. The tests were performed with the new laser this time despite the fact that if it was a success the new laser would not be used in conjunction with the apparatus. The first set of tests were done with the front surfaced mirrors, this was done in order to get the best reflection possible despite the drawback of lower motor efficiency. However this did not prove to be a success, with the same result as before being observed. Even though the test with the front surfaced mirrors had been a failure and it was assumed that the tests with also be a failure as a result it was decided to continue with testing the plastic mirrors for the sake of good practice. However this also proved to be a failure, exhausting the only rational for why the lissajous figures were not being produced. At this point with no additional theories for why the apparatus is failing to fulfill its purpose and given the fact that it was near halfway through the third week of practical work, which was more time than had been allowed for this piece of apparatus to be built, it was


decided that the best course of action was to abandon it for the time being and return to it if and when there was time available at the end of the project. However due to the time it took to work on the next two pieces of apparatus this did not occur.

3.2 CONSTRUCTION OF APPARATUS; STANDING WAVES IN A TUBE OF GAS

The construction of this apparatus began with acquiring the metal tube. It was not necessary to purchase this as this experiment had been done years before and the tube was still in the lab. The tube measured approximately 1.03 metres in length and had an internal diameter of 37 mm, and as the tube had been used for this experiment before it already had holes drilled along its length. These were about1 mm in diameter and spaced about 2 cm apart, however a number of the holes had been blocked with some kind of filler, presumably for use in another role. As it had been sometime since the tube had been used for its intended purpose it was necessary to give it a substantial clean. The filler was removed from the hole using a Stanley blade and 1mm drill bit, after this the entire outside and inside the ends of the tube was rubbed down with emery paper in order to remove small bits of dirt which had become stuck to it. Once the tube was cleaned the end which the gas was to flow in through had to be sealed, this was to be done by soldering a copper disc into the end with a nozel which would allow the gas in. The first step was to cut the disc down tothe right diameter to fit the hole, this was done using the lathe. Then a hole was drilled in the disc for the nozzle to fit into. Before any of the pieces could be soldered together it all had to be cleaned using emery paper. When it was cleaned the end of the nozzle and the hole in the disc were giving a coat of flux in order to allow the solder to better adhere to these surfaces. Then a lining of solder was applied to outside of the nozzle and the inside of the hole, when the solder on both had cooled they were fit together and the solder was melted using a small propane torch, this allowed the solder on both pieces to melt and for a tight seal. However when it came time to fit the disc and nozzle into the tube it proved far more difficult to do. The reason for this being that as the area on he nozzle and hole it was to fit were fairly small it was relatively easy to apply the solder to them but the outside of the disc had a much larger diameter and it proved far more difficult to get an even coat of solder around the disc. Despite the fact that a metal to metal seal at this end of the tube would have been far more secure it had to be abandoned as it could not be achieved with the facilities in the lab.In place of the metal to metal seal a rubber bung was to be used. Although this necessitated that the two holes closest to that end of the tube be sealed with solder in order to stop the bung from melting or catching fire. To allow gas to flow through the bung a hole was drilled through its centre and a small pipe was put through it, a larger gas hose, commonly seen in the lab, could be attached to this then to allow gas to flow. To ensure that the gas could be turned off at a moments notice a flow control valve was added to the apparatus this was place along the gas line ahead of the tube. It was connected to the gas hose using the same type of tubing which connected the gas hose to the larger tube. The next step was to make a mount for the tube so it would stay in place while in use. This was done by cutting a triangle out of the top of a pice of mdf and the cutting a small rectangle out the bottom. Then a rectangle the same size was cut out of a second, smaller piece of mdf so as the two could slot together, when the was done it provided a solid square base. See Figure 17. Two of these were made so the tube could be supported by one at either end. When the tube was no longer rolling on the bench a speaker could be mounted to the tube. It was decided to first try to mount the speaker directly to the tube without the rubber diaphragm. To do this a speaker with approximately the same diameter as the tube was fixed onto the end of the tube using the hot glue gun. As the only other thing which would need to be done was to connect the speaker to a signal generator, the apparatus was ready to be tested.

10 mm

80 mm40 mm

120 mm


FIGURE 17. However withing a few seconds of lighting the gas a leak was detected in the flow control valve and the gas had to turned. This reason for the leak was that the tubing connecting the valve was the wrong size and so it had to be remove from the system, leaving the gas to be operated by switching it on and off using the tap on the bench. Once the valve was removed and the test was begun again a second leak was detected at the speaker which caused the glue holding it in place to catch fire. To stop this damaging the speaker the gas was quickly switched off and the fire extinguished. Instead of risking this happening again it was decided that it would be better to have the rubber diaphragm in place as this garunteed that there would be zero leaks at that end of the tube. This meant that the speaker had to be cut of using a small so that the diaphragm could be put in place. When the speaker was removed it and the end of the tube was cleaned to remove any excess glue which was left in place. When the glue was removed the piece of rubber taken from a latex glove was strtched over the aperture and fixed in place using masking tape, the reason masing tape was chosen was that when the tube became hot it wouldn't melt like some other tapes may have. After the rubber diaphragm was secured the spaker was fitted against it and propped in place so as the apparatus could be tested again. After there were no leaks detected the signal generator was switched on and different frequencies were sent down the tube, however no standing wave was observed at any point. To try and affect a standing wave in the tube the fundamental frequency, f,of the tube was worked out using the equation;

f= nv4 (L+0.4d )

Equation (1)

Where, v, is the speed of sound in air, n, is the resonant node, this must be an odd number for a closed tube, L, is the lenght of the tube and d, is the internal diameter of the tube. The fundamental frequency was calculated to be about 78 Hz but when this frequency was applied there was still no evidence of a standing wave in the tube. At this point it was assumed that the problem was that the speaker did not have enough power to transmit the signal through the rubber diaphragm effectively, to combat this the speaker was replaced with a much larger one. However when this was tested it also failed to generate a standing wave. At this point it was uncertain in what way th signal could be effectively transmittied until it was theorized that by fixing a ping pong ball to the front of the speaker and then placing this in contact with the diaphragm the signal could be transmitted more effectively. So a ping pong ball was acquired and glued to the front of the speaker, the speaker was then put in front of the tube with the ball in contact with the diaphragm as proposed. The gas was then turned on and the set up tested.


This time there was a success of a sort, while a standing wave could not be distinguished clearly, there were definite changes visible as the frequency was changed. Instead of continuing to try and achieve a perfect standing wave, it was decided that musics would be put through the tube now, as this was fairly simple to do and there was less than a week left of practical work left with one piece of apparatus left to build. To put music through the tube it was simply a matter of soldering two wires to a mini-jack and then putting some heat shrink sleeve of the wires and the end of the jack to secure them together, then two crocodile clips were soldered onto the loose ends of the wires so as cables could connect them to signal generator which the music would have to go through in order to played out of the speaker. When this was done an MP3 player was connected to the signal generator and then music form it played in the tube providng a variation of pressure jumps in the tube characterized by different height flames springing up along its lenght.


CHAPTER 4: DISCUSSION & CONCLUSION

CONTENTS

4.1 Discussion4.2 Conclusion

4.1 DISCUSSION

As the outcome of this project did not involve the analysis of any data, I will instead use this section to discuss the problems that arose during the project and alternative solutions to ones which were attempted. Beginning with the first piece of apparatus to be built, the 'Laser Show', the two significant problems with this were, one, the pen laser being used was not visible once the motors were in motion and two, when the more powerrful laser was being used lissajous figures were still not being produced. While building the apparatus I assumed that the laser was simply not powerful enough, which proved to contain some truth, as shown by the fact that the more powerful laser was visible up to about four feet away from the mirror. However upon reflecting after the practical work was over, I realised that the power of the laser could not have been the true issue, as even the more powerful laser only reached out a small distance when reflected between the two rotating mirrors when ordinarily it could reach out many meters and still be clearly visible to anyone close enough to view the dot. The more powerful laser was simply able to overcome the true problem because it had more power and even then only to a limited extent. As I can no longer test the apparatus to determine the true problem, I am only able to theorize what it may have been. It is my belief that it was the velocity at which the mirrors were rotating which resulted in the laser light being dispersed at the first mirror before it could all be transmitted and then again at the second mirror. The logic behind my theory is that as the more powerful laser emits more intense light then it is less effected by the dispersion. The only was I can think to test this if I had the opportunity would be to replace the class 2 laser with a class 3 laser and see if the beam from this reaches out ay further, but as I can not test this it can only remain a theory. The only other theory that I can offer as to why the light is not being transmitted is that it is being absorbed by the mirror material, however this seems unlikely as when the mirrors are not rotating there is no issue with the light being transmitted. So while I am sure that the mirror material is absorbing some of the light I do not believe that this is the problem with the transmission of the beam. The problem involving lissajous figures not being produced is a little trickier to solve. The leading theory as far as I am concerned is also to do with the velocity at which the motors are turning, this time I believe that the ratio of velocities between the motors is not been controlled accurately enough. This may seem like a small detail but in fact the ratio between the frequencies is one of the most important aspects of producing lissajous figures. The best solution to this problem in my opinion would be to use a stepper motor, the velocity of which can be accurately control. This would involve constructing a circuit board for the motor which would need to be programmed, but i believe that this would yield much better results assuming my theory is corrct. However in truth I believe that the only way that this piece of apparatus could be constructed successfully is if it were a project onto itself, this way as each problem occured it could be addressed appropriatley instead of in a rushed manner. The problems occuring with the 'standing waves in a tube of gas' apparatus were relatively small in comparison to the 'Laser Show'. These problems required more time than serious thought and were more of matter of 'fiddling' with the apparatus than making any sweeping changes to the design. For instance the problem with leaks in the system would have been just a matter of acquiring appropriate sized fittings for the hosing and flow control valve and the problem with the


transmission of the signal through the rubber diaphragm could have been addressed more efficiently if it weren't for the time constraints, this simply would have been a matter of as I said earlier 'fiddling' and perhaps some more calculations. Unfortunately due to my own poor time management I was unable to give the time I needed to this problem and it was left with a quick fix. Similarly due to poor time management I was unable to begin construction of the 'standing wave on a string' apparatus, and was only able to test the possible ways in which the standing wave could be generated. However having acknowledged my own poor time management I believe that if this project were to be attempted it again it would be better served by cutting down the number of pieces of apparatus to be constructed.

4.2 CONCLUSION

As the goal of this project was to construct three pieces of working apparatus, I in truth failed to achieve that goal however I do not believe that the project as a whole was a failure, two pieces of apparatus were constructed which as opposed to being completely malfuntioning require only a moderate amount of tinkering to become functional. The reason for this goal cannot be forgotten either as industry grows on a global scale every year it has never been more important to have people qualified in physics and while it would be nice if these people were to obtain their qualification from DIT in truth it is more important that they have simply chosen to study physics and that was ultimately the goal of constructing these pieces of apparatus, that they be shown to public, and that they intice people to study physics.


APPENDIX:

CONTENTS

List of Tables and FiguresTable of Components; Lissajous Figures with laser lightTable of Components; Standing Waves in a tube of gas

LIST OF TABLES AND FIGURES:

Figure 1. – Diagram of Cathode Ray Tube’s internal components [1]Figure 2. – Diagram of Sawtooth Waveform [1]Figure 3A. – Diagram of Lissajous Figure, Right Diagonal Figure 3B. – Diagram of Lissajous Figure, Left DiagonalFigure 3C. – Diagram of Lissajous Figure, CircleFigure 3D. – Diagram of Lissajous Figure, EclipseFigure 3E. – Diagram of Lissajous Figure, CrownFigure 4. – Diagram Laser Pumping Figure 5. – Diagram of Demonstrating Optical FeedbackFigure 6. – Table displaying pathological effects with associated laser wavelengthsFigure 7. – Diagram of proposed design for apparatus; Lissajous figures with laser lightFigure 8. – Circuit Diagram, Lissajous figures with laser lightFigure 9. – Diagram displaying a standing waveFigure 10. – Diagram displaying nodes and antinodesFigure 11. – Diagram displaying different harmonics of a waveFigure 12. – Diagram of proposed design for apparatus; Standing Waves in a tube of gasFigure 13A. – Diagram showing possible design for turning circular motion into linear motionFigure 13B. – Diagram showing another possible design for turning circular motion into linear motionFigure 14. – Diagram showing design for turning circular motion into linear motionFigure 15. – Diagram of proposed apparatus; Standing waves on a stringFigure 16A. – Diagram showing motor mountingFigure 16B. – Diagram showing laser mountingFigure 17. – Diagram showing elevation and side view of mounts for Ruben’s tube


TABLE OF COMPONENTS; LISSAJOUS FIGURES WITH LASER LIGHT

Component Quantity NotesDC Motor 2 1.5 – 3 VPotentiometer 2 100 ΩClass I Laser 1 3 VDPDT Switch 2 n/aSPST Switch 1 n/aD Battery + Holder 2 n/aPlastic Mirror 2 50 mm diameterPlastic Rod 2 20 mm length, 10 mm diameterMotor, Laser Mount 3 49 x 49 x 12 mmBase Board 1 400 x 176 x 1 mmWiring n/a n/aHeat Shrink Sleeve n/a n/a

Components used in place of those listed above

Component Quantity NotesClass II Laser 1 12 – 15 VGlass Front-surfaced Mirror 2 50 mm diameter

TABLE OF COMPONENTS; STANDING WAVES IN A TUBE OF GAS

Component Quantity NotesMetal Tube 1 1.03 m length, 37 mm internal diameterLoudspeaker 1 n/aRubber bung 1 n/aFlow control valve 1 n/aRubber Diaphragm 1 n/aMini-jack 1 n/aCrocodile Clip 2 n/aPing Pong ball 1 n/aWooden Support 2 n/aHosing n/a 1 mWiring n/a n/aHeat Shrink Sleeve n/a n/a


REFERENCES:[1] DIT 2nd Year Physics Manual, Experiment 3, The Cathode Ray Oscilloscope

[2] http://www.ngsir.netfirms.com/englishhtm/Lissajous.htm, 17/5/10

[3] Optics Notes, Lasers, John Doran, DIT

[4] http://nobelprize.org/educational_games/physics/laser/facts/applications.html, 18/5/10

[5] http://en.wikipedia.org/wiki/Laser_safety, 18/5/10

[6] http://hyperphysics.phy-astr.gsu.edu/hbase/waves/standw.html, 18/5/10

[7] http://www.physicsclassroom.com/class/waves/u10l4c.cfm, 18/5/10

[8] http://en.wikipedia.org/wiki/Harmonic, 19/5/10

[9] http://www.iopireland.org/activity/education/Science_on_Stage/Physics_on_Stage_3/file_19141.pdf, 14/5/10

[10] http://www.iopireland.org/activity/education/Science_on_Stage/Physics_on_Stage_3/file_19140.pdf, 14/5/10

http://www.iopireland.org/activity/education/Science_on_Stage/Physics_on_Stage_3/file_19140.pdf

http://www.iopireland.org/activity/education/Science_on_Stage/Physics_on_Stage_3/file_19141.pdf

http://en.wikipedia.org/wiki/Harmonic

http://www.physicsclassroom.com/class/waves/u10l4c.cfm

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/standw.html

http://en.wikipedia.org/wiki/Laser_safety

http://nobelprize.org/educational_games/physics/laser/facts/applications.html

http://www.ngsir.netfirms.com/englishhtm/Lissajous.htm

Documents

Design and Construction of Physics Demonstration Equipment