4 Waves Student Check/ Feedback

Unit 4 Longitudinal and Transverse WavesLearning

Outcomes

To be able explain the differences between longitudinal and transverse wavesTo know examples of eachTo be explain what polarisation is and how it proves light is a transverse wave

Waves All waves are caused by oscillations and all transfer energy without transferring matter. This means that a sound wave can transfer energy to your eardrum from a far speaker without the air particles by the speaker moving into your ear. We will now look at the two types of waves and how they are different

Longitudinal Waves Here is a longitudinal wave; the oscillations are parallel to the direction of propagation (travel). Where the particles are close together we call a compression and where they are spread we call a rarefaction. The wavelength is the distance from one compression or rarefaction to the next. The amplitude is the maximum distance the particle moves from its equilibrium position to the right of left.

Transverse Waves

Here is a transverse wave; the oscillations are perpendicular

to the direction of propagation.Where the particles are displaced above the equilibrium position we call a peak and below we call a trough.The wavelength is the distance from one peak or trough to the next.The amplitude is the maximum distance the particle moves from its equilibrium position up or down.

Examples: water

waves, Mexican

waves and waves of the EM spectrum

EM waves are produced from varying electric and magnetic field.

PolarisationPolarisation restricts the oscillations of a wave to one plane. In the diagrams the light is initially oscillating in all directions. A piece of Polaroid only allows light to oscillate in the same direction as it.

In the top diagram the light passes through a vertical plane Polaroid and becomes polarized in the vertical plane. This can then pass through the second vertical Polaroid.In the middle diagram the light becomes polarized in the horizontal

plane.In the bottom diagram the light becomes vertically polarized but this cannot pass through a horizontal plane Polaroid.

This is proof that the waves of the EM spectrum are transverse waves. If they were longitudinal waves the forwards and backwards motion would not be stopped by crossed pieces of Polaroid; the bottom set up would emit light.

ApplicationsTV aerials get the best reception when they point to the transmission source so they absorb the maximum amount of the radio waves.

Unit 4 Superposition and Standing WavesLearning

Outcomes

To know and be able to explain what standing waves are and how they are formedTo know what nodes and antinodes areTo be able to sketch the standing wave produced at different frequencies

SuperpositionHere are two waves that have amplitudes of 1.0 travelling in opposite directions:

Superposition is the process by which two waves combine into a single wave form when they overlap.If we add these waves together the resultant depends on where the peaks of the waves are compared to each other. Here are three examples of what the resultant could be: a wave with an amplitude of 1.5, no resultant wave at all and a wave with an amplitude of 2.0

Stationary/Standing WavesWhen two similar waves travel in opposite directions they can superpose to form a standing (or stationary) wave. Here is the experimental set up of how we can form a standing wave on a string. The vibration generator sends waves down the string at a certain frequency, they reach the end of the string and reflect back at the same frequency. On their way back the two waves travelling in opposite direction superpose to form a standing wave made up of nodes and antinodes.

Nodes Positions on a standing wave which do not vibrate. The waves combine to give zero displacement

Antinodes Positions on a standing wave where there is a maximum displacement.

Standing Waves Progressive WavesAmplitude Maximum at antinode and zero at nodes The same for all parts of the waveFrequency All parts of the wave have the same frequency All parts of the wave have the same frequencyWavelength Twice the distance between adjacent nodes The distance between two adjacent peaksPhase All points between two adjacent nodes in phase Points one wavelength apart in phaseEnergy No energy translation Energy translation in the direction of the waveWaveform Does not move forward Moves forwards

HarmonicsAs we increase the frequency of the vibration generator we will see standing waves being set up. The first will occur when the generator is vibrating at the fundamental frequency, f0, of the string.

First Harmonic f = f0 λ = 2 L2 nodes and 1 antinode

Second Harmonic f = 2f0 λ = L3 nodes and 2 antinodes

Third Harmonic f = 3f0 λ = ⅔ L4 nodes and 3 antinodes

Forth Harmonic f = 4f0 λ = ½ L

Unit 4 The OscilloscopeLearning

Outcomes

To know what are the main controls of the oscilloscopeTo be able to determine the voltage and current using an oscilloscopeTo be able to determine the time period and frequency using an oscilloscope

The OscilloscopeAn oscilloscope can be used to show the sizes of voltages and currents in both d.c. and a.c. circuits. This is what a typical oscilloscope looks like. A trace would be seen on the grid display.

D.C. Traces (Also seen in GCSE Physics 2)If we connected a battery or cell to an oscilloscope, we would see a trace similar to the one shown here. The current of a d.c. supply is constant, this means the voltage is constant. We see a straight line.

A.C. Traces (Also seen in GCSE Physics 2)

If we connect anything that draws power from the Mains to an oscilloscope we will see a similar trace to the one shown here. The current is constantly changing from maximum flow in one direction to maximum flow in the other direction; this means the voltage is doing the same.We see a wave.

ControlsThere are two main controls that we use are the volts/div and time base dials:The volts/div (volts per division) dial allows you to change how much each vertical square is worth.The time base dial allows you to change how much each horizontal square is worth.

VoltageWe can measure the voltage of a d.c. supply by counting the number or vertical squares from the origin to the line and then multiplying it by the volts/div. In the trace the line is 2.5 squares above 0, if each square is worth 5 volts the voltage is (2.5 x 5) 12.5 volts.We can measure the peak voltage of an a.c. supply by counting how many vertical squares from the centre of the wave to the top and then multiplying it by the volts/div (how much voltage each square is worth). In the trace the peak voltage is 4 squares high, if each square is worth 5 volts the voltage is (4 x 5) 20 volts.

Time and FrequencyWe can measure the time for one period (wave) by counting how many horizontal squares one wavelength is and then multiplying it by the time base (how much time each square is worth).In the trace above one wave is 6 squares long, if each square is worth 0.02 seconds the time for one wave is 0.12 seconds.We can calculate the frequency (how many waves or many times this happens per second) using the equation:

f = 1T and

T=1f

If the time period is 0.12 seconds, the frequency is 8.33Hz

Practical Phase Difference of PendulumsYou are going to carry out an experiment to investigate how

the time between two pendulum moving in phase depends on their relative lengths.

Equipment ListPendulum bob (x2)String (2 x 1.5m)Rulers (1m)Clamp Stands, Bosses and ClampsStop clockPlasticine

Task Clamp a ruler between two clamp stands and

suspend two pendulums of equal length approximately 1.00 m.

Attach a second clamp to one of the clamp stands so that it obstructs the swing of the second pendulum.

Set the initial value of y to by 0.20m. Measure the lengths L and y and state the

precision of your readings. Displace and release the pendulums so they

oscillate with a small amplitude parallel to the edge of the bench.

Start the timer when the two pendulum motions are seen to be exactly in phase.

Measure and record the time until the pendulums are next seen to be in phase, T.

Repeat this reading three times. Measure and record further values of T which

correspond to four larger values of y. Record your results in a table with a column

√ LL− y .

After the ExperimentWhat were the dependent and independent variables in your investigation?Look at your graph, are the results reliable? Why?Other than taking repeat readings how else could you increase the reliability of your experiment?

Plot a graph of √ LL− y (on the y-axis) against

1T (on

the x-axis)Draw a line of best fit for your graph.Calculate the gradient of this line.

Calculate the uncertainty in the measurement for the value of T when y has a value of 0.20 m.Calculate this as a percentage uncertainty of the mean value of T for this value of y.Calculate the uncertainty in the measurement for the value of T for your largest value of y.Calculate this as a percentage uncertainty of the mean value of T for this value of y.

A student suggests that in order to extend the investigation additional measurements of T should be made using values of y that were much smaller than 0.20 m and much bigger than 0.90 m. Discuss briefly whether you think that such additional readings would improve the quality of the evidence obtained for the experiment

Analysis Sound Waves in a Column of AirA speaker was attached to the top of an open ended glass cylinder. The other end was placed in a trough of water so

that the column of air between the speaker and the water is 15 cm. The speaker is attached to a signal generator which is adjusted until each harmonic is heard

Experimental DataHere are the frequencies recorded for the first five harmonics.

Harmonic Frequency, f (Hz) Wavelength, λ (m)

First 1134 1131 1125

Second 2288 2282 2291

Third 3387 3407 3406

Forth 4838 4841 4850

Fifth 5639 5666 5645

HarmonicMean Frequency, f

(Hz)Wavelength, λ (m)

1λ (m-1)

Wave Speed, v (m/s)

First

Second

Third

Forth

Fifth

AnalysisCalculate the mean frequency for each harmonic.Calculate the uncertainty in the frequency of the first harmonic.What is this as a percentage of the mean frequency?Calculate the uncertainty in the frequency of the third harmonic.What is this as a percentage of the mean frequency?Calculate the uncertainty in the frequency of the fifth harmonic.What is this as a percentage of the mean frequency?

Calculate the wavelength of the standing wave for each harmonic.

Complete the column in the table labelled

1λ .

Plot a graph of f on the y axis against

1λ on the x axis.

Draw a line of best fit and calculate the gradient.Calculate the percentage difference between the gradient and the accepted value of 343 m/s.

Use the equation v=fλ to complete the last column of the table.Calculate your mean value for the wave speed v.What is the uncertainty in the wave speed?Calculate the percentage difference between your mean value and the accepted value.

Is the gradient value or the table value of v more accurate?

What type of error is responsible for the spread of frequencies for each harmonic?

Chapter 4 Exam Practice Questions1 a Define the amplitude of a wave.

(1 mark)

b i Other than electromagnetic radiation, give one example of a wave that is transverse.

(1 mark)

ii State one difference between a transverse wave and a longitudinal wave.

(1 mark)

c Figure 1 shows two identical polarising filters, A and B, and an unpolarised light source. The arrows indicate the plane in which the electric field of the wave oscillates.i If polarised light is reaching the observer, draw the direction of the transmission

axis on filter B in Figure 1.

Figure 1(1 mark)

ii The polarising filter B is rotated clockwise through 360° about line XY from the position shown in Figure 2. On the axes below, sketch how the light intensity reaching the observer varies as this is done.

Figure 2(2 marks)

d State one application, other than in education, of a polarising filter and give a reason for its use.

(2 marks)

From AQA Physics A PHYA2 Mechanics, Materials and Waves June 2010 (Question 3)

2 Ultrasound waves are used to produce images of a foetus inside a womb.a Explain what is meant by the frequency of a wave.

(1 mark)

b Ultrasound is a longitudinal wave. Describe the nature of a longitudinal wave.

(2 marks)

c To produce an image with sufficient detail, the wavelength of the ultrasound must be 0.50 mm. The speed of the ultrasound in body tissue is 1540 m s–1. Calculate the frequency of the ultrasound at this wavelength.Give your answer to an appropriate number of significant figures.

frequency Hz(2 marks)

From AQA Physics A PHYA2 Mechanics, Materials and Waves June 2014 (Question 7)

3 Figure 3a shows a side view of a string on a guitar. The string cannot move at either of the two bridges when it is vibrating. When vibrating at its first harmonic, the frequency of the sound produced is 108 Hz.a i On Figure 3a, sketch the stationary wave produced when the string is vibrating

at its first harmonic.

Figure 3a(1 mark)

ii Calculate the wavelength of the first harmonic mode of vibration.

answer m(2 marks)

iii Calculate the speed of a progressive wave on this string.

answer m s–1

(2 marks)

b While tuning the guitar, the guitarist produces a harmonic that has a node 0.16 m from bridge A.i On Figure 3b, sketch the stationary wave produced and label all nodes that are

present.

Figure 3b

(2 marks)ii Calculate the frequency of the harmonic.

answer Hz(1 mark)

c The guitarist needs to raise the first harmonic frequency of vibration of this string.State one way in which this can be achieved.

(1 mark)

From AQA Physics A PHYA2 Mechanics, Materials and Waves January 2010 (Question 4)

4 Figure 4 shows two ways in which a wave can travel along a slinky spring.

Figure 4

a State and explain which wave is longitudinal.

(2 marks)

b On Figure 4,i clearly indicate and label the wavelength of wave B

(1 mark)

ii use arrows to show the direction in which the points P and Q are about to move as each wave moves to the right.

(2 marks)

c Electromagnetic waves are similar in nature to wave A.Explain why it is important to align the aerial of a television correctly to receive the strongest signal.

(2 marks)

From AQA Physics A PHYA2 Mechanics, Materials and Waves June 2012 (Question 7)

4 When a note is played on a violin, the sound it produces consists of the first harmonic and many higher harmonics.Figure 5a shows the shape of the string for a stationary wave that corresponds to one of these higher harmonics. The positions of maximum and zero displacement for one harmonic are shown. Points A and B are fixed. Points X, Y, and Z are points on the string.

Figure 5a

a i Describe the motion of point X.

(2 marks)

ii State the phase relationship between

X and Y

X and Z

(2 marks)b The frequency of this harmonic is 780 Hz.

i Show that the speed of a progressive wave on this string is about 125 m s–1.

(2 marks)

ii Calculate the time taken for the string at point Z to move from maximum displacement back to zero displacement.

answer s(3 marks)

c The violinist presses on the string at C to shorten the part of the string that vibrates.Figure 5b shows the string between C and B vibrating at its first harmonic. The length of the whole string is 320 mm and the distance between C and B is 240 mm.

Figure 5b

i State the name given to the point on the wave midway between C and B.

(1 mark)

ii Calculate the wavelength of this stationary wave.

answer m(2 marks)

iii Calculate the frequency of this first harmonic. The speed of the progressive wave remains at 125 m s–1.

answer Hz(1 mark)

From AQA Physics A PHYA2 Mechanics, Materials and Waves June 2012 (Question 6)

Chapter 4 Exam Practice Answers

Question Answer Marks Guidance

1 a Maximum displacement from equilibrium / mean position / midpoint / etc.

1

1 b i Any one from: surface of water / water waves / in ripple tank rope slinky clearly qualified as transverse secondary (S) waves

Max1

1 b ii For a transverse wave the oscillation (of the medium) is perpendicular to wave travel 1

Question Answer Marks Guidance

or a transverse wave can be polarisedor all longitudinal waves require a medium.

1 c i Vertical line (in place of polarising film) on B ± 5° 1

1 c ii

Maxima at 0, 180, and 360, minima at 90 and 270 and line reaches same minimum and maximum every time and reasonable shape.

2

1 d Appropriate use Reason for polarising filter being used, for example:

Polarising glasses / sunglasses / windscreens

to reduce glare

Camera to reduce glare / enhance image

(In a) microscope to identify minerals or rocks

Polarimeter to analyse chemicals / concentration or type of sugar

Stress analysis to reveal areas of high and low stress / other relevant detail

LCD displays very low power / other relevant detail

3D glasses to enhance viewing experience, etc.

2

From AQA Physics A PHYA2 Mechanics, Materials and Waves mark scheme June 2010 (Question 3)

Total 8

2 a Number of (complete) waves (passing a point) in 1 sORnumber of waves / time (for the waves to pass a point)OR(complete number of) oscillations / vibrations per secondOR1T with T defined as time for 1 (complete) oscillation

1 Allow: CyclesAllow: Unit time

2 b For two marks:Oscillation of particles / medium / material / etc. (but not oscillation of wave)is parallel to / in same direction asthe direction wave (travels).

For one mark:Particles / material / medium move(s) / disturbance / displacementparallel to / in same direction asthe direction wave travels

2 Allow: VibrationAllow: Direction of energy transfer / wave propagation.

Question Answer Marks GuidanceOR(oscillations) parallel to direction of wave travel.

A one mark answer with:mention of compressions and rarefactionsOR(longitudinal waves) cannot be polarisedGets two marks

2 c

f

15400 .50×10–3 3 100 000 (Hz) (3 080 000)

Two significant figures

2

Total 5

From AQA Physics A PHYA2 Particles, Quantum Phenomena and Electricity mark scheme June 2014 (Question 7)

3 a i One loop (accept single line only, accept single dashed line)Nodes at each bridge (± length of arrowhead)Antinode at centre

1

3 a ii λ0 2L or λ 0.64 2 1.3 (m) (1.28) 2

3 a iii (c fλ) 108 a ii 138 to 140(.4) (m s–1) ecf from a ii 2

3 b i Four antinodes (single or double line)First node on 0.16 m (within width of arrowhead)Middle node between the decimal point and the centre of the ‘m’ in ‘0.64 m’Middle three nodes labelled ‘N’, ‘n’ or ‘node’

2

3 b ii (4 f0 ) 430 (Hz) (432)

or use of f

vλ gives 430 to 440 Hz

1 Correct answer only, no e.c.f.

3 c Decrease the length / increase tension / tighten string 1

Total 9

From AQA Physics A PHYA2 Mechanics, Materials and Waves mark scheme January 2010 (Question 4)

4 a (Wave) B (The parts of the) spring oscillate / move back and forth in direction of / parallel to wave travelORmention of compressions and rarefactions.

2Second mark can only be scored if first mark is scored.

4 b i (Double-ended arrow / line / brackets) from between two points in phase 1

4 b ii Wave A: arrow vertically upwards Wave B: arrow horizontally to the left

2 Arrow on point P pointing upwards on the diagram of wave A.Arrow on point Q pointing to the left on diagram of wave B.

4 c (Transmitted radio waves are often) polarised. Aerial (rods) must be aligned in the same plane (of polarisation / electric field) of the wave.

2

Question Answer Marks Guidance

Total 7

From AQA Physics A PHYA2 Mechanics, Materials and Waves mark scheme June 2012 (Question 7)

5 a i It oscillates / vibrates (allow: goes up and down / side to side / etc., repeatedly, continuously, etc.)about equilibrium position / perpendicularly to central line.

2

5 a ii X and Y: Antiphase / 180 (degrees out of phase) / π (radians out of phase) X and Z: In phase / zero (degrees) / 2π (radians)

2

5 b i v fλ

780×0 .322 or 780 0.16

OR

780×3202 or 780 160

124.8 (m s–1)

2

This is an independent mark.Correct answer to four significant figures

5 b ii 14 cycle

T

1780 OR 1.28 10–3

0.25 1.28 10–3

3.2 10–4 (s) ORAllow correct alternative approach using distance of 0.04 m

travelled by progressive wave in

14 cycle divided by speed.

0 .04125 3.2 10–4 (s)

3

5 c i Antinode 1

5 c ii 2 0.240 0.48 m 480 m gets 1 mark out of 2 2

5 c iii

(f

vλ 124.8 or

1250 .48 ) 260 (Hz) ecf from c ii

1

Total 13

From AQA Physics A PHYA2 Mechanics, Materials and Waves mark scheme June 2012 (Question 6)