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Page 1 of 42 3.4 Waves - Interference 2 – Questions Q1. A gravimeter is an instrument used to measure the acceleration due to gravity. The gravimeter measures the distance fallen by a free-falling mirror in a known time. To do this, monochromatic light is reflected normally off the mirror, creating interference between the incident and reflected waves. The mirror is released from rest and falls, causing a change in the phase difference between the incident and reflected waves at a detector. At the point of release of the mirror, the waves are in phase, resulting in a maximum intensity at the detector. The next maximum is produced at the detector when the mirror has fallen through a distance equal to half a wavelength of the light. The gravimeter records the number of maxima detected in a known time as the mirror falls. These data are used by the gravimeter to compute the acceleration of the free-falling mirror. Figure 1 illustrates the phase relationship between the incident and reflected waves at the detector for one position of the mirror. Figure 1 (a) Show that the wavelength of the light is 600nm. (3) (b) Determine the phase difference, in rad, between the incident and reflected waves shown in Figure 1. phase difference = ____________________________ rad (2)

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Page 1: 3.4 Waves - Interference 2 - Qs3.4 Waves - Interference 2 – Questions . Q1. A gravimeter is an instrument used to measure the acceleration due to gravity. The gravimeter measures

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3.4 Waves - Interference 2 – Questions

Q1. A gravimeter is an instrument used to measure the acceleration due to gravity. The gravimeter measures the distance fallen by a free-falling mirror in a known time.

To do this, monochromatic light is reflected normally off the mirror, creating interference between the incident and reflected waves. The mirror is released from rest and falls, causing a change in the phase difference between the incident and reflected waves at a detector.

At the point of release of the mirror, the waves are in phase, resulting in a maximum intensity at the detector. The next maximum is produced at the detector when the mirror has fallen through a distance equal to half a wavelength of the light. The gravimeter records the number of maxima detected in a known time as the mirror falls. These data are used by the gravimeter to compute the acceleration of the free-falling mirror.

Figure 1 illustrates the phase relationship between the incident and reflected waves at the detector for one position of the mirror.

Figure 1

(a) Show that the wavelength of the light is 600 nm. (3)

(b) Determine the phase difference, in rad, between the incident and reflected waves shown in Figure 1.

phase difference = ____________________________ rad (2)

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(c) A maximum is detected each time the mirror travels a distance equal to half a wavelength of the light.

In one measurement 2.37 × 105 maxima are recorded as the mirror is released from rest and falls for 0.120 s.

Using an appropriate equation of motion, calculate the acceleration due to gravity that the gravimeter computes from these data.

State your answer to 3 significant figures.

wavelength of the light = 600 nm

acceleration due to gravity = ____________________________ m s–2

(3)

(d) Figure 2 is a graph that the gravimeter could produce to show how the distance travelled by the mirror varies with time as it falls.

Figure 2

Determine the gradient of the line when the time is 0.12 s.

gradient = ____________________________ (2)

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(e) State what this gradient represents.

___________________________________________________________________ (1)

(Total 11 marks)

Q2. (a) The diagram below shows schematically an arrangement for producing interference

fringes using a double slit.

A dark fringe (minimum intensity) is observed at the point labelled P.

(i) Show clearly on the diagram the distance that is equal to the path difference between the light rays from the two slits to the point P.

(1)

(ii) Explain how the path difference determines that the light intensity at point P is a minimum.

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________ (3)

(iii) Explain briefly the role of diffraction in producing the interference patterns (You may draw a sketch to support your explanation if you wish.)

______________________________________________________________

______________________________________________________________

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______________________________________________________________

______________________________________________________________ (2)

(b) In one experiment the separation of the slits is 4.0 × 10–4 m. The distance from the slits to the screen is 0.60 m.

Calculate the distance between the centres of two adjacent dark fringes when light of wavelength 5.5 × 10–7 m is used.

(2)

(c) A student has learned that electrons behave like waves and decides to try demonstrate this using the arrangement in the diagram above. The lamp is replaced by a source of electrons and the system is evacuated.

The student accelerates the electrons to a velocity of 1.4 × 106 m s–1. The beam of electrons is then incident on the double slits. The electrons produce light when incident on the screen.

mass of an electron = 9.1 × 10–31 kg Planck constant = 6.6 × 10–34 J s

(i) Calculate the de Broglie wavelength associated with the electrons. (3)

(ii) Explain briefly, with an appropriate calculation, why the student would be unsuccessful in demonstrating observable interference using the slit separation of 4.0 × 10–4 m.

______________________________________________________________

______________________________________________________________ (2)

(Total 13 marks)

Q3. The diagram shows two closely spaced narrow slits illuminated by light from a single slit in front of a monochromatic light source. A microscope is used to view the pattern of bright and dark fringes formed by light from the two slits.

(a) (i) Explain qualitatively why these fringes are formed.

______________________________________________________________

______________________________________________________________

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______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

(ii) Describe what is observed if one of the narrow slits is covered by an opaque object.

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________ (8)

(b) The microscope is replaced by a fibre-optic detector linked to a computer. The detector consists of the flat end of many optical fibres fixed together along a line. The other end of each optical fibre is attached to a light-sensitive diode in a circuit connected to a computer. The signal to the computer from each diode is in proportion to the intensity of light incident on the diode. The computer display shows how the intensity of light at the detector varies along the line of the detector when both of the narrow slits are open.

(i) Describe and explain how the pattern on the display would change if the slit separation were increased.

______________________________________________________________

______________________________________________________________

______________________________________________________________

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______________________________________________________________

______________________________________________________________

(ii) Each fibre consists of a core of refractive index 1.50 surrounded by cladding of refractive index 1.32. Calculate the critical angle at the core-cladding boundary.

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

(iii) The diagram below shows a light ray entering an optical fibre at point P on the flat end of the fibre. The angle of incidence of this light ray at the core-cladding boundary is equal to the critical angle. On the diagram, sketch the path of another light ray from air, incident at the same point P, which is totally internally reflected at the core-cladding boundary.

(7)

(Total 15 marks)

Q4. The figure below shows a spectrometer that uses a diffraction grating to split a beam of light into its constituent wavelengths and enables the angles of the diffracted beams to be measured.

(a) Give one possible application of the spectrometer and diffraction grating used in this way.

___________________________________________________________________

___________________________________________________________________

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(1)

(b) (i) When the spectrometer telescope is rotated from an initial angle of zero degrees, a spectrum is not observed until the angle of diffraction θ is about 50°. State the order of this spectrum.

______________________________________________________________ (1)

(ii) White light is directed into the spectrometer. Light emerges at A and B. State one difference between the light emerging at B compared to that emerging at A.

______________________________________________________________

______________________________________________________________

______________________________________________________________ (1)

(c) The angle of diffraction θ at the centre of the observed beam B in the image above is 51.0° and the grating has 1480 lines per mm.

Calculate the wavelength of the light observed at the centre of beam B.

wavelength ____________________ m (3)

(d) Determine by calculation whether any more orders could be observed at the wavelength calculated in part (c).

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(2)

(Total 8 marks)

Q5. The diagram shows two identical loudspeakers, A and B, placed 0.75 m apart. Each loudspeaker emits sound of frequency 2000 Hz.

Point C is on a line midway between the speakers and 5.0 m away from the line joining the speakers. A listener at C hears a maximum intensity of sound. If the listener then moves from C to E or D, the sound intensity heard decreases to a minimum. Further movement in the same direction results in the repeated increase and decrease in the sound intensity. speed of sound in air = 330 m s–1

(a) Explain why the sound intensity

(i) is a maximum at C,

______________________________________________________________

______________________________________________________________

______________________________________________________________

(ii) is a minimum at D or E.

______________________________________________________________

______________________________________________________________

______________________________________________________________ (4)

(b) Calculate

(i) the wavelength of the sound,

______________________________________________________________

______________________________________________________________

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(ii) the distance CE.

______________________________________________________________

______________________________________________________________

______________________________________________________________ (4)

(Total 8 marks)

Q6. The diagram for this question is drawn to scale and 1 mm on the diagram represents an actual distance of 5 mm.

S1 and S2 are identical coherent transmitters emitting, in phase, microwaves with a wavelength of 25 mm. They are positioned 250 mm apart on a horizontal surface and a detector can be placed anywhere along the line YY' which is in the same plane as the transmitters and parallel to the line containing S1 and S2.

(a) Explain what is meant by coherent.

___________________________________________________________________

___________________________________________________________________ (2)

(b) By making measurements on the diagram and using the scale, determine the number of wavelengths in the path

(i) S1R,

______________________________________________________________

______________________________________________________________

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(ii) S2R.

______________________________________________________________

______________________________________________________________

(iii) Use your answers to (i) and (ii) to determine whether or not you expect the signal received by a detector placed at R to be a maximum. Explain your answer.

______________________________________________________________

______________________________________________________________

______________________________________________________________ (5)

(c) Describe how you would expect the signal strength to vary as the detector is moved from R to P via Q.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________ (2)

(d) Calculate the frequency of the microwaves.

___________________________________________________________________

___________________________________________________________________ (1)

(Total 10 marks)

Q7. A laser illuminates a pair of slits of separation 0.24 mm. The wavelength of light from the laser is 6.3 × 10–7 m. Interference fringes are observed on a screen 4.3 m from the slits.

(a) Calculate the fringe separation. Give an appropriate unit for your answer.

fringe separation ____________________ (3)

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(b) State the conditions necessary for two light sources to be coherent.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________ (2)

(Total 5 marks)

Q8. A diffraction grating has 300 lines per mm. It is illuminated with monochromatic light of wavelength 540 nm. Calculate the angle of the 2nd order maximum, giving your answer to the appropriate number of significant figures.

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

angle ____________________ degrees (Total 4 marks)

Q9. (a) State what is meant by coherent sources of light.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________ (2)

(b)

Figure 1

Young’s fringes are produced on the screen from the monochromatic source by the arrangement shown in Figure 1.

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You may be awarded marks for the quality of written communication in your answers.

(i) Explain why slit S should be narrow.

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

(ii) Why do slits S1 and S2 act as coherent sources?

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________ (4)

(c) The pattern on the screen may be represented as a graph of intensity against position on the screen. The central fringe is shown on the graph in Figure 2. Complete this graph to represent the rest of the pattern by drawing on Figure 2.

Figure 2 (2)

(Total 8 marks)

Q10. Just over two hundred years ago Thomas Young demonstrated the interference of light by illuminating two closely spaced narrow slits with light from a single light source.

(a) What did this suggest to Young about the nature of light?

___________________________________________________________________

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___________________________________________________________________ (1)

(b) The demonstration can be carried out more conveniently with a laser. A laser produces coherent, monochromatic light.

(i) State what is meant by monochromatic.

______________________________________________________________

______________________________________________________________

(ii) State what is meant by coherent.

______________________________________________________________

______________________________________________________________ (2)

(iii) State one safety precaution that should be taken while using a laser.

______________________________________________________________

______________________________________________________________ (1)

(c) The diagram below shows the maxima of a two slit interference pattern produced on a screen when a laser was used as a monochromatic light source.

The slit spacing = 0.30 mm. The distance from the slits to the screen = 10.0 m.

Use the diagram above to calculate the wavelength of the light that produced the pattern.

answer = ____________________ m

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(3)

(d) The laser is replaced by another laser emitting visible light with a shorter wavelength. State and explain how this will affect the spacing of the maxima on the screen.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________ (2)

(Total 9 marks)

Q11. Short pulses of sound are reflected from the wall of a building 18 m away from the sound source. The reflected pulses return to the source after 0.11 s.

(a) Calculate the speed of sound.

Speed of sound ____________________ (3)

(b) The sound source now emits a continuous tone at a constant frequency. An observer, walking at a constant speed from the source to the wall, hears a regular rise and fall in the intensity of the sound. Explain how the minima of intensity occur.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________ (3)

(Total 6 marks)

Q12. A laser emits light of wavelength 6.3 × 10–7 m and is used to illuminate a double slit which has a separation of 2.4 × 10–4 m. Interference fringes are observed 4.2 m from the slits.

(a) Calculate the fringe separation. (2)

(b) The double slit acts as a pair of coherent sources. Explain what is meant by coherent sources.

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___________________________________________________________________

___________________________________________________________________

___________________________________________________________________ (2)

(c) The diagram shows the light from the slits, S1 and S2, meeting at P where the first dark fringe is observed.

Explain why a dark fringe is observed at P.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________ (3)

(Total 7 marks)

Q13. The diagram below shows a laboratory ultrasound transmitter emitting ultrasonic waves through two slits placed 0.20 m apart. A receiver, moving along line AB, parallel to the line of the slits, detects regular rises and falls in the strength of the signal. A student measures a distance of 0.22 m between the first and the third maxima in the signal when the receiver is 2.5 m from the slits.

(a) (i) Calculate the distance between successive maxima.

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Distance between successive maxima ____________________ (1)

(ii) Calculate the wavelength of the ultrasonic waves.

Wavelength ____________________ (2)

(b) One of the slits is now covered. No other changes are made to the experiment.

State the differences between the observations made as the receiver is moved along AB before and after this change. Explain the changes that you mention.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________ (3)

(Total 6 marks)

Q14. A narrow beam of monochromatic red light is directed at a double slit arrangement. Parallel red and dark fringes are seen on the screen shown in the diagram above.

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(a) (i) Light passing through each slit spreads out. What is the name for this effect?

______________________________________________________________ (1)

(ii) Explain the formation of the fringes seen on the screen.

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________ (4)

(iii) The slit spacing was 0.56 mm. The distance across 4 fringe spacings was 3.6 mm when the screen was at a distance of 0.80 m from the slits. Calculate the wavelength of the red light.

Answer ____________________ m (4)

(b) Describe how the appearance of the fringes would differ if white light had been used instead of red light.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

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___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________ (3)

(Total 12 marks)

Q15. A laser is used with a double slit positioned 5.0 m from a white screen. The separation of the slits is 0.25 mm and the wavelength of the laser light is 630 mm.

The screen is removed and a linear air track positioned so that a glider on the air track moves in the same plane that was occupied by the screen.

A light dependent resistor, LDR, is attached to a glider and connected by loosely hanging leads to a datalogger. When the glider moves at a constant speed, the datalogger records the output voltage from a circuit containing the LDR. Output from the datalogger, plotted against time, is shown below.

(a) (i) Explain why the LDR output voltage varies with the position of the glider.

______________________________________________________________

______________________________________________________________

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______________________________________________________________

(ii) Calculate the separation between two adjacent positions of the glider when the LDR is under maximum illumination.

______________________________________________________________

______________________________________________________________

______________________________________________________________

(iii) Use your answer to (ii) and the graph to calculate a speed for the glider consistent with these results.

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________ (5)

(b) A potential divider current is used to derive an output from the LDR.

In this experiment the resistance of the LDR is 10 kΩ when under maximum illumination and 100 kΩ when under minimum illumination. The value of R is 50 Ω. Calculate the values of V1 and V2 shown on the graph and state which corresponds to maximum illumination.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________ (3)

(c) If the experiment were to be repeated how could you ensure that the glider is launched with the same speed each time?

___________________________________________________________________

___________________________________________________________________

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___________________________________________________________________ (2)

(Total 10 marks)

Q16. The diagram below shows an arrangement used to demonstrate the interference of sound waves. The two loudspeakers act as coherent sources of sound.

(a) Explain what is meant by the term coherent sources.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________ (2)

(b) In the diagram, the loudspeakers are separated by 8.5 m and are emitting sound of wavelength 0.77 m. When a sound engineer walks along the line AB, 65 m from the loudspeakers, he observes a regular rise and fall in the sound intensity.

(i) Explain this observation.

______________________________________________________________

______________________________________________________________

______________________________________________________________ (2)

(ii) Calculate the distance moved along AB between two consecutive maxima of sound.

Distance moved ____________________ (2)

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(Total 6 marks)

Q17. The diagram below shows the paths of microwaves from two narrow slits, acting as coherent sources, through a vacuum to a detector.

(a) Explain what is meant by coherent sources.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________ (2)

(b) (i) The frequency of the microwaves is 9.4 GHz.

Calculate the wavelength of the waves.

wavelength = ____________________ m

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(2)

(ii) Using the diagram above and your answer to part (b)(i), calculate the path difference between the two waves arriving at the detector.

path difference = ____________________ m (1)

(c) State and explain whether a maximum or minimum is detected at the position shown in the diagram above.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________ (3)

(d) The experiment is now rearranged so that the perpendicular distance from the slits to the detector is 0.42 m. The interference fringe spacing changes to 0.11 m.

Calculate the slit separation. Give your answer to an appropriate number of significant figures.

slit separation = ____________________ m (3)

(e) With the detector at the position of a maximum, the frequency of the microwaves is now doubled. State and explain what would now be detected by the detector in the same position.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________ (3)

(Total 14 marks)

Q18.

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An interference pattern is produced using monochromatic light from two coherent sources. The separation of the two sources is 0.25 mm and the fringe separation is 7.8 mm. The interference pattern is observed on a screen that is 3.5 m from the sources.

(a) Calculate the wavelength of the light used to produce the interference pattern.

wavelength ____________________ (3)

(b) The figure below shows light from two coherent sources, S1 and S2, superimposing to create a bright fringe at point Q. Q is equidistant from S1 and S2. The diagram is not to scale.

Explain how the dark fringe at the point P is caused.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________ (3)

(Total 6 marks)

Q19. The diagram shows Young’s double-slit experiment performed with a tungsten filament lamp as the light source.

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(a) On the axes in the diagram above, sketch a graph to show how the intensity varies with position for a monochromatic light source.

(2)

(b) (i) For an interference pattern to be observed the light has to be emitted by two coherent sources. Explain what is meant by coherent sources.

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________ (1)

(ii) Explain how the use of the single slit in the arrangement above makes the light from the two slits sufficiently coherent for fringes to be observed.

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________ (1)

(iii) In this experiment light behaves as a wave. Explain how the bright fringes are formed.

______________________________________________________________

______________________________________________________________

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______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________ (3)

(c) (i) A scientist carries out the Young double-slit experiment using a laser that emits violet light of wavelength 405 nm. The separation of the slits is 5.00 × 10–5 m.

Using a metre ruler the scientist measures the separation of two adjacent bright fringes in the central region of the pattern to be 4 mm.

Calculate the distance between the double slits and the screen.

distance = ____________________ m (2)

(ii) Describe the change to the pattern seen on the screen when the violet laser is replaced by a green laser. Assume the brightness of the central maximum is the same for both lasers.

______________________________________________________________

______________________________________________________________

______________________________________________________________ (1)

(iii) The scientist uses the same apparatus to measure the wavelength of visible electromagnetic radiation emitted by another laser. Describe how he should change the way the apparatus is arranged and used in order to obtain an accurate value for the wavelength.

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

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______________________________________________________________

______________________________________________________________

______________________________________________________________ (3)

(Total 13 marks)

Q20. For a plane transmission diffraction grating, the diffraction grating equation for the first order beam is:

λ = d sin θ

(a) The figure below shows two of the slits in the grating. Label the figure below with the distances d and λ.

(2)

(b) State and explain what happens to the value of angle θ for the first order beam if the wavelength of the monochromatic light decreases.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________ (2)

(c) A diffraction grating was used with a spectrometer to obtain the line spectrum of star X shown in the figure below. Shown are some line spectra for six elements that have been obtained in the laboratory.

Place ticks in the boxes next to the three elements that are present in the atmosphere of star X.

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(2)

(d) The diffraction grating used to obtain the spectrum of star X had 300 slits per mm.

(i) Calculate the distance between the centres of two adjacent slits on this grating.

answer = ______________________ m (1)

(ii) Calculate the first order angle of diffraction of line P in the figure above.

answer = ______________________ degrees (2)

(Total 9 marks)

Q21. Musicians can use tuning forks to tune their instruments. A tuning fork produces a specific frequency when it vibrates.

Figure 1 shows a tuning fork vibrating in air at a single instant in time. The circles represent the positions of air particles in the sound wave.

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Figure 1

(a) The tuning fork emits a wave that has a frequency of 0.51 kHz.

(i) State the meaning of the term frequency of a wave.

______________________________________________________________ (1)

(ii) Air particles vibrate in different phases in the direction in which the wave is travelling.

Calculate the minimum separation of particles that vibrate 180° out of phase.

speed of sound in air = 340 m s–1

minimum separation ____________________ m (3)

(b) A student sets a tuning fork of lower frequency vibrating at the same time as the 0.51 kHz tuning fork in part (a).

The student detects the resultant sound wave with a microphone. The variation with time of the voltage generated by the microphone is shown in Figure 2.

Figure 2

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(i) Explain why the two tuning forks are not coherent sources of sound waves.

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______________________________________________________________ (2)

(ii) Explain why the resultant sound has a minimum amplitude at 50 ms.

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______________________________________________________________ (3)

(iii) Calculate the frequency of the tuning fork that emits the lower frequency.

frequency ____________________ Hz (3)

(c) A signal generator connected to a loudspeaker produces a sinusoidal sound wave with a frequency of 440 Hz.

The variation in air pressure with time for this sound is shown in Figure 3.

Figure 3

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A violin string has a fundamental frequency (first harmonic) of 440 Hz.

Figure 4 shows the variation in air pressure with time for the sound created by the violin string.

Figure 4

(i) The two sounds have the same pitch but sound different.

What term describes the difference between the sounds heard? Tick () the correct answer.

Frequency modulation

Octaves

Path difference

Quality (1)

(ii) The complex sound in Figure 4 can be electronically synthesised.

Describe the process of electronically synthesising this sound.

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(Total 16 marks)

Q22. This question is about an experiment to measure the wavelength of microwaves.

A microwave transmitter T and a receiver R are arranged on a line marked on the bench.

A metal sheet M is placed on the marked line perpendicular to the bench surface.

Figure 1 shows side and plan views of the arrangement. The circuit connected to T and the ammeter connected to R are only shown in the plan view.

Figure 1

The distance y between T and R is recorded.

T is switched on and the output from T is adjusted so a reading is produced on the ammeter as shown in Figure 2.

Figure 2

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M is kept parallel to the marked line and moved slowly away as shown in Figure 3.

Figure 3

The reading decreases to a minimum reading which is not zero. The perpendicular distance x between the marked line and M is recorded.

(a) The ammeter reading depends on the superposition of waves travelling directly to R and other waves that reach R after reflection from M.

State the phase difference between the sets of waves superposing at R when the ammeter reading is a minimum. Give a suitable unit with your answer.

___________________________________________________________________ (1)

(b) Explain why the minimum reading is not zero when the distance x is measured.

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(c) When M is moved further away the reading increases to a maximum then decreases to a minimum.

At the first minimum position, a student labels the minimum n = 1 and records the value of x. The next minimum position is labelled n = 2 and the new value of x is recorded. Several positions of maxima and minima are produced.

Describe a procedure that the student could use to make sure that M is parallel to the marked line before measuring each value of x.

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You may wish to include a sketch with your answer.

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___________________________________________________________________ (2)

(d) It can be shown that

where λ is the wavelength of the microwaves and y is the distance defined in Figure 1.

The student plots the graph shown in Figure 4.

The student estimates the uncertainty in each value of to be 0.025 m and adds error bars to the graph.

Determine • the maximum gradient Gmax of a line that passes through all the error bars • the minimum gradient Gmin of a line that passes through all the error bars.

Gmax = ____________________

Gmin = ____________________ (3)

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(e) Determine λ using your results for Gmax and Gmin.

λ = ____________________ m (2)

Figure 4

(f) Determine the percentage uncertainty in your result for λ.

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percentage uncertainty in λ = ____________________ % (3)

(g) Explain how the graph in Figure 4 can be used to obtain the value of y. You are not required to determine y.

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(h) Suppose that the data for n = 13 had not been plotted on Figure 4.

Add a tick () in each row of the table to identify the effect, if any, on the results you would obtain for Gmax, Gmin, λ and y.

Result Reduced Not affected increased

Gmax

Gmin

λ

y

(4) (Total 18 marks)

Q23. (a) A double slit interference experiment is set up in a laboratory using a source of

yellow monochromatic light of wavelength 5.86 × 10–7 m. The separation of the two vertical parallel slits is 0.36 mm and the distance from the slits to the plane where the fringes are observed is 1.80 m.

(i) Describe the appearance of the fringes.

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(ii) Calculate the fringe separation, and also the angle between the middle of the central fringe and the middle of the second bright fringe.

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(iii) Explain why more fringes will be seen if each of the slits is made narrower, assuming that no other changes are made.

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______________________________________________________________ (8)

(b) Light of wavelength 5.86 × 10–7 m falls at right angles on a diffraction grating which has 400 lines per mm.

(i) Calculate the angle between the straight through image and the first order image.

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(ii) Determine the highest order image which can be seen with this arrangement.

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______________________________________________________________ (5)

(c) Give two reasons why the diffraction grating arrangement is more suitable for the accurate measurement of the wavelength of light than the two-slit interference arrangement.

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(Total 15 marks)

Q24. A student has a diffraction grating that is marked 3.5 × 103 lines per m.

(a) Calculate the percentage uncertainty in the number of lines per metre suggested by this marking.

percentage uncertainty = ____________________ % (1)

(b) Determine the grating spacing.

grating spacing = ____________________ mm (2)

(c) State the absolute uncertainty in the value of the spacing.

absolute uncertainty = ____________________ mm (1)

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(d) The student sets up the apparatus shown in Figure 1 in an experiment to confirm the value marked on the diffraction grating.

Figure 1

The laser has a wavelength of 628 nm. Figure 2 shows part of the interference pattern that appears on the screen. A ruler gives the scale.

Figure 2

Use Figure 2 to determine the spacing between two adjacent maxima in the interference pattern. Show all your working clearly.

spacing = ____________________ mm (1)

(e) Calculate the number of lines per metre on the grating.

number of lines = ____________________ (2)

(f) State and explain whether the value for the number of lines per m obtained in part (e) is in agreement with the value stated on the grating.

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___________________________________________________________________

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(g) State one safety precaution that you would take if you were to carry out the experiment that was performed by the student.

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(Total 10 marks)

Q25. Read through the following passage and answer the questions that follow it.

Measuring the speed of sound in air 5 10

After the wave nature of sound had been identified, many attempts were made to measure its speed in air. The earliest known attempt was made by the French scientist Gassendi in the 17th century. The procedure involved timing the interval between seeing the flash of a gun and hearing the bang from some distance away. Gassendi assumed that, compared with the speed of sound, the speed of light is infinite. The value he obtained for the speed of sound was 480 m s–1. He also realised that the speed of sound does not depend on frequency. A much better value of 350 m s–1 was obtained by the Italian physicists Borelli and Viviani using the same procedure. In 1740 another Italian, Bianconi, showed that sound travels faster when the temperature of the air is greater. In 1738 a value of 332 m s–1 was obtained by scientists in Paris. This is remarkably close to the currently accepted value considering the measuring equipment available to the scientists at that time. Since 1986 the accepted value has been 331.29 m s–1 at 0 °C.

(a) Suggest an experiment that will demonstrate the wave nature of sound (line 1).

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(b) Using Gassendi’s value for the speed of sound (line 6), calculate the time between seeing the flash of a gun and hearing its bang over a distance of 2.5 km.

time = ____________________ s

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(1)

(c) Explain why it was necessary to assume that ‘compared with the speed of sound, the speed of light is infinite’ (line 5).

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(d) Explain one observation that could have led Gassendi to conclude that ‘the speed of sound does not depend on frequency’ (line 7).

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(e) Explain how the value obtained by Borelli and Viviani was ‘much better’ than that obtained by Gassendi (line 8).

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(f) The speed of sound c in dry air is given by

where θ is the temperature in °C, and k is a constant.

Calculate a value for k using data from the passage.

k = ____________________ m s–1 K–½

(2)

(g) State the steps taken by the scientific community for the value of a quantity to be ‘accepted’ (line 13).

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___________________________________________________________________

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___________________________________________________________________ (2)

(Total 10 marks)

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