· Web viewThe diagram below shows a hammer being struck against the end of a horizontal metal rod. A pulse of sound travels along the rod from where the hammer strikes it to the

Colonel Frank Seely School

Exampro A-level Physics (7407/7408) 3.3.1.1 Progressive waves

Name:

Class:

Author:

Date:

Time: 218

Marks: 184

Comments:

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Q1.Two waves with amplitudes a and 3a interfere.

The ratio is

A 2

B 3

C 4

D infinity(Total 1 mark)

Q2.Monochromatic light passes from air into water. Which one of the following statements is true?

A The velocity, frequency and wavelength all change

B The velocity and frequency change but not the wavelength

C The velocity and wavelength change but not the frequency

D The frequency and wavelength change but not the velocity

(Total 1 mark)

Q3.The diagram below is an arrangement for analysing the light emitted by a source.

(a) Suggest a light source that would emit a continuous spectrum.

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........................................................................................................................(1)

(b) The light source emits a range of wavelengths from 500 nm to 700 nm. The light is incident on a diffraction grating that has 10 000 lines per metre.

(i) Calculate the angle from the straight through direction at which the first order maximum for the 500 nm wavelength is formed.

Angle = ........................................(3)

(ii) Calculate the angular width of the first order spectrum.

Angular width ........................................(1)

(iii) The detector is positioned 2.0 m from the grating. Calculate the distance between the extreme ends of the first order spectrum in this position.

Distance = ........................................(1)

(c) The single slit is initially illuminated by light from a point source that is 0.02 m from the slit.

State and explain how the intensity of light incident on the single slit changes when the light source is moved to a position 0.05 m from the slit.

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........................................................................................................................(4)

(Total 10 marks)

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Q4.The intensity of a sound is 1.9 × 10–8 W m–2 at a distance of 0.25 km from the source. Calculate the intensity of the sound at a distance of 0.75 km from the source.

Intensity of sound ....................................(Total 3 marks)

Q5.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.

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........................................................................................................................(3)

(Total 6 marks)

Q6. The diagram below shows three wavefronts of light directed towards a glass block in the air. The direction of travel of these wavefronts is also shown.

Complete the diagram to show the position of these three wavefronts after partial reflection and refraction at the surface of the glass block.

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(Total 3 marks)

Q7. (a) Figure 1 shows how the displacement s of the particles in a medium carrying a pulse of ultrasound varies with distance d along the medium at one instant.

Figure 1

(i) State the amplitude of the wave.

...............................................................................................................(1)

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(ii) The speed of the wave is 1200 m s–1. Calculate the frequency of oscillation of the particles of the medium when the ultrasound wave is travelling through it.

Frequency of oscillation ..........................................(3)

(b) An ultrasound transmitter is placed directly on the skin of a patient. Figure 2 shows the amplitudes of the transmitted pulse and the pulse received after reflection by an organ in the body. amplitude

Figure 2

(i) Give two possible reasons why the amplitude of the received pulse is lower than that which is transmitted.

Reason 1 ..............................................................................................

...............................................................................................................

Reason 2 ..............................................................................................

...............................................................................................................(2)

(ii) The speed of ultrasound in body tissue is 1200 m s–1. Calculate the depth of the reflecting surface below the skin.

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Depth of reflecting surface ......................................(2)

(Total 8 marks)

Q8. The diagram below shows a hammer being struck against the end of a horizontal metal rod. A pulse of sound travels along the rod from where the hammer strikes it to the far end and back again. The sound pulse throws the hammer and rod apart when it returns. An electrical timing circuit measures the time for which the hammer and the rod are in contact.

(a) Circle the word below that describes the type of wave that travels along the rod.

transverse longitudinal(1)

(b) State the name of the effect that causes the sound pulse to return to the hammer.

........................................................................................................................(1)

(c) The rod is 0.45 m long and the time for which the hammer is in contact with the rod is 1.6 × 10–4 s. Calculate the speed of sound in the rod.

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Speed of sound ...................................................(3)

(Total 5 marks)

Q9. A square metre of the Moon’s surface that is perpendicular to sunlight receives 1.4 kJ of energy every second from the Sun. Estimate the total energy radiated by the Sun every second assuming that the Sun acts as a point source.

mean distance of the Moon from the Sun = 1.5 × 1011 m

Total energy radiated .........................................(Total 3 marks)

Q10. (a) With the aid of a clearly labelled diagram explain how a sound wave in air transmits energy away from its source.

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........................................................................................................................(3)

(b) Unlike sound waves, transverse waves can be polarised. Give one example of a transverse wave and draw a diagram to show how it can be plane polarised. State a method of polarising a wave of the type you have chosen.

Example transverse wave ........................................

Method of polarisation .......................................................(3)

(Total 6 marks)

Q11. The graph in Figure 1 shows the results of an investigation of how the visible light intensity I varies with distance d from a filament lamp. The lamp can be assumed to behave as a point source of light.

Figure 1

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(a) Use data from the graph to show that the visible light intensity varies with distance according to an inverse square law.

(3)

(b) Find the power of the visible light emitted by the filament lamp.

power ..........................................(2)

(Total 5 marks)

Q12. Figure 1 shows three particles in a medium that is transmitting a sound wave. Particles A and C are separated by one wavelength and particle B is half way between them when no sound is being transmitted.

Figure 1

(a) Name the type of wave that is involved in the transmission of this sound.

........................................................................................................................(1)

(b) At one instant particle A is displaced to the point A' indicated by the tip of the arrow in Figure 1. Show on Figure 1 the displacements of particles B and C at the same instant. Label the position B' and C' respectively.

(1)

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(c) Explain briefly how energy is transmitted in this sound wave.

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........................................................................................................................(2)

(Total 4 marks)

Q13. Figure 1 shows the displacement of particles in an ultrasound wave at different distances from the source at a particular time. The wave travels at 3200 m s–1.

Figure 1

(a) (i) Use the graph to find the wavelength of the wave in Figure 1.

wavelength .........................................

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(ii) Calculate the frequency of the ultrasound wave.

frequency ...........................................(3)

(b) One industrial use for ultrasound waves is to detect flaws inside a metal block. Figure 2a shows the arrangement in which the waves are fired downwards in short pulses from a transmitter. Figure 2b shows the amplitudes of the initial pulse and the reflected signals recorded by the receiver. You may assume that there is no reflected pulse received from the upper surface of the block.

Figure 2a

Figure 2b

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The ultrasound wave travels at 3200 m s–1. Use data from Figure 2b to calculate the distance of the flaw below the top of the block.

distance ................................(3)

(Total 6 marks)

Q14.The least distance between two points of a progressive transverse wave which have a

phase difference of rad is 0.050 m. If the frequency of the wave is 500 Hz, what is the speed of the wave?

A 25 m s–1

B 75 m s–1

C 150 m s–1

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D 1666 m s–1

(Total 1 mark)

Q15.Explain the differences between an undamped progressive transverse wave and a stationary transverse wave, in terms of (a) amplitude, (b) phase and (c) energy transfer.

(a) amplitude

progressive wave ...........................................................................................

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stationary wave ..............................................................................................

........................................................................................................................

(b) phase


........................................................................................................................

stationary wave ..............................................................................................

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(c) energy transfer


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stationary wave ..............................................................................................

........................................................................................................................(Total 5 marks)

Q16.(a) For a sound wave travelling through air, explain what is meant by particle displacement, amplitude and wavelength.

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Particle displacement ....................................................................................

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amplitude .......................................................................................................

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wavelength .....................................................................................................

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........................................................................................................................(4)

(b)

Graph A shows the variation of particle displacement with time at a point on the path of a progressive wave of constant amplitude.

Graph B shows the variation of particle displacement with distance along the same wave at a particular instant.

(i) Show on graph A

(1) the wave amplitude, a,

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(2) the period, T, of the vibrations providing the wave.

(ii) Show on graph B

(1) the wavelength of the wave, λ,

(2) two points, P and Q, which are always π/2 out of phase.(4)

(Total 8 marks)

Q17.A progressive wave in a stretched string has a speed of 20 m s−1 and a frequency of 100 Hz.What is the phase difference between two points 25 mm apart?

A zero

B rad

C rad

D π rad(Total 1 mark)

Q18.A wave motion has period T, frequency f, wavelength λ and speed ʋ. Which one of the following equations is incorrect?

A 1 = Tf

B T =

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C λ =

D Tʋ = λ(Total 1 mark)

Q19.(a) The diagram shows the apparatus required for a simple experiment to measure the speed of sound.

A pulse of sound is sent down a hollow glass tube and is reflected at the sealed end of the tube. A microphone, M, placed at the open end detects the initial pulse and, at a later time, the reflected pulse. The microphone is connected to an oscilloscope which gives a signal when the microphone detects a pulse of sound.

The signal displayed on the oscilloscope screen is shown below.

If the time base of the oscilloscope is set to 2.0 ms per division, estimate the speed of sound in air.

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(3)

(b) Describe how the frequency of a sinusoidal alternating (ac) voltage source is measured using an oscilloscope.

Your answer should include a sketch of the trace seen on the oscilloscope screen and explain how the frequency is obtained from this trace.

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(Total 8 marks)

Q20.The audible range of a girl's hearing is 30 Hz to 16 500 Hz. If the speed of sound in air is 330 m s−1, what is the shortest wavelength of sound in air which the girl can hear?

A m

B m

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C m

D m(Total 1 mark)

Q21.

displacement

The graph shows, at a particular instant, the variation of the displacement of the particles in a transverse progressive water wave, of wavelength 4 cm, travelling from left to right. Which one of the following statements is not true?

A The distance PS = 3 cm.

B The particle velocity at Q is a maximum.

C The particle at S is moving downwards

D Particles at P and R are in phase.(Total 1 mark)

Q22.A source emits light of wavelength 600 nm as a train of waves lasting 0.01 µs. How many complete waves are sent out?speed of light = 3 × 108 m s−1

A 5 × 106

B 18 × 107

C 5 × 109

D 5 × 1022

(Total 1 mark)

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Q23.A wave of frequency 5 Hz travels at 8 km s–1 through a medium. What is the phase difference, in radians, between two points 2 km apart?

A0

B

Cπ

D(Total 1 mark)

Q24.Which line, A to D, in the table gives a correct difference between a progressive wave and a stationary wave?

progressive wave stationary wave

A all the particles vibrate some of the particles do notvibrate

B none of the particles vibratewith the same amplitude

all the particles vibrate withthe same amplitude

C all the particles vibrate inphase with each other

none of the particles vibrate inphase with each other

D some of the particles do notvibrate

all the particles vibrate inphase with each other

(Total 1 mark)

Q25.Two points on a progressive wave differ in phase by . The distance between them is 0.5 m, and the frequency of the oscillation is 10 Hz. What is the minimum speed of the wave?

A 0.2 m s−1

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C 10 m s−1

C 20 m s−1

D 40 m s−1

(Total 1 mark)

Q26.The speed of sound in water is 1500 m s−1. For a sound wave in water having frequency

2500 Hz, what is the minimum distance between two points at which the vibrations are rad out of phase?

A 0.05 m

B 0.10 m

C 0.15 m

D 0.20 m(Total 1 mark)

Q27.The diagram shows a snapshot of a wave on a rope travelling from left to right.

At the instant shown, point P is at maximum displacement and point Q is at zero displacement.Which one of the following lines, A to D, in the table correctly describes the motion of P and Q in the next half-cycle?

P Q

A falls then rises rises

B falls then rises rises then falls

C falls falls

D falls rises then falls

(Total 1 mark)

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Q28. An aerial system consists of a horizontal copper wire of length 38 m supported between two masts, as shown in the figure below. The wire transmits electromagnetic waves when an alternating potential is applied to it at one end.

(a) The wavelength of the radiation transmitted from the wire is twice the length of the copper wire. Calculate the frequency of the transmitted radiation.

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......................................................................................................................(1)

(b) The ends of the copper wire are fixed to masts of height 12.0 m. The masts are held in a vertical position by cables, labelled P and Q, as shown in the figure above.

(i) P has a length of 14.0 m and the tension in it is 110 N. Calculate the tension in the copper wire.

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(ii) The copper wire has a diameter of 4.0 mm. Calculate the stress in the copper wire.

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(iii) Discuss whether the wire is in danger of breaking if it is stretched further due to movement of the top of the masts in strong winds.

breaking stress of copper = 3.0 × 108 Pa

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(Total 8 marks)

Q29. (a) The diagram below represents a progressive wave travelling from left to right on a stretched string.

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(i) Calculate the wavelength of the wave.

answer ................................... m(1)

(ii) The frequency of the wave is 22 Hz. Calculate the speed of the wave.

answer............................m s–1

(2)

(iii) State the phase difference between points X and Y on the string, giving an appropriate unit.

answer ..............................(2)

(b) Describe how the displacement of point Y on the string varies in the next half-period.

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(Total 7 marks)

Q30. Figure 1 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 in its fundamental mode the frequency of the sound produced is 108 Hz.

(a) (i) On Figure 1, sketch the stationary wave produced when the string is vibrating in its fundamental mode.

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Figure 1

(1)

(ii) Calculate the wavelength of the fundamental mode of vibration.

answer = ........................................... m(2)

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

answer = ...................................... m s–1

(2)

(b) While tuning the guitar, the guitarist produces an overtone that has a node 0.16 m from bridge A.

(i) On Figure 2, sketch the stationary wave produced and label all nodes that are present.

Figure 2

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(2)

(ii) Calculate the frequency of the overtone.

answer = ...................................... Hz(1)

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

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......................................................................................................................(1)

(Total 9 marks)

Q31. (a) Define the amplitude of a wave.

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......................................................................................................................(1)

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

.............................................................................................................(1)

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

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.............................................................................................................(1)

(c) The figure below 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 the figure below.

(1)

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

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(2)

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

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(Total 8 marks)

Q32. The figure below shows a continuous progressive wave on a rope. There is a knot in the rope.

(a) Define the amplitude of a wave.

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........................................................................................................................(2)

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(b) The wave travels to the right.Describe how the vertical displacement of the knot varies over the next complete cycle.

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(c) A continuous wave of the same amplitude and frequency moves along the rope from the right and passes through the first wave. The knot becomes motionless.Explain how this could happen.

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(Total 8 marks)

Q33. The figure below shows two ways in which a wave can travel along a slinky spring.

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(a) State and explain which wave is longitudinal.

........................................................................................................................

........................................................................................................................(2)

(b) On the figure above,

(i) clearly indicate and label the wavelength of wave B(1)

(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)

(c) Electromagnetic waves are similar in nature to wave A.

Explain why it is important to correctly align the aerial of a TV in order to receive the strongest signal.

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................(2)

(Total 7 marks)

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Q34. When a note is played on a violin, the sound it produces consists of the fundamental and many overtones.

Figure 1 shows the shape of the string for a stationary wave that corresponds to one of these overtones. The positions of maximum and zero displacement for one overtone are shown. Points A and B are fixed. Points X, Y and Z are points on the string.

Figure 1

(a) (i) Describe the motion of point X.

...............................................................................................................

...............................................................................................................

...............................................................................................................

...............................................................................................................(2)

(ii) State the phase relationship between

X and Y .................................................................................................

X and Z .................................................................................................(2)

(b) The frequency of this overtone is 780 Hz.

(i) Show that the speed of a progressive wave on this string is about 125 ms–1.

(2)

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

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answer = ................................... s(3)

(c) The violinist presses on the string at C to shorten the part of the string that vibrates.Figure 2 shows the string between C and B vibrating in its fundamental mode. The length of the whole string is 320 mm and the distance between C and B is 240 mm.

Figure 2

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

...............................................................................................................(1)

(ii) Calculate the wavelength of this stationary wave.

answer = ................................... m(2)

(iii) Calculate the frequency of this fundamental mode. The speed of the progressive wave remains at 125 ms–1.

answer = .................................Hz(1)

(Total 13 marks)

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Q35. When a note is played on a violin, the sound it produces consists of the fundamental and many overtones.

Figure 1 shows the shape of the string for a stationary wave that corresponds to one of these overtones. The positions of maximum and zero displacement for one overtone are shown. Points A and B are fixed. Points X, Y and Z are points on the string.

Figure 1

(a) (i) Describe the motion of point X.

...............................................................................................................

...............................................................................................................

...............................................................................................................

...............................................................................................................(2)

(ii) State the phase relationship between

X and Y .................................................................................................

X and Z .................................................................................................(2)

(b) The frequency of this overtone is 780 Hz.

(i) Show that the speed of a progressive wave on this string is about 125 ms–1.

(2)

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

answer = ................................... s(3)

(c) The violinist presses on the string at C to shorten the part of the string that vibrates.Figure 2 shows the string between C and B vibrating in its fundamental mode. The length of the whole string is 320 mm and the distance between C and B is 240 mm.

Figure 2

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

...............................................................................................................(1)

(ii) Calculate the wavelength of this stationary wave.

answer = ................................... m(2)

(iii) Calculate the frequency of this fundamental mode. The speed of the progressive wave remains at 125 ms–1.

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answer = .................................Hz(1)

(Total 13 marks)

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M1.A[1]

M2.C[1]

M3.(a) filament lamp / sun etc.B1

(1)

(b) (i) d = 1.0 × 10–4 mC1

use of λ = dsin θ or substituted valuesC1

θ1 = 0.286° / 0.29°A1

(3)

(ii) Δθ = 0.115° (c.a.o.)B1

(1)

(iii) width = 4.0 × 10–3 m or 3.9 × 10–3 m (e.c.f. for 2 × sin (b(ii))or 2 × tan (b(ii)); allow 1 s.f.)

B1(1)

(c) lower intensityC1

because energy spreadsC1

use or statement of inverse square lawC1

ratio 0.16 or falls by factor of 6.25 c.a.o.A1

(4)

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[10]

M4.use of inverse-square lawC1

3 × distance so 1 / 9 × intensity (or equivalent calc)C1

1.9 × 10–8 / 9 = 2.11 × 10–9 Wm–2

A1[3]

M5.(a) distance travelled = 2 × 18 mC1

Speed = 36 / 0.11M1

= 327 m / s [164 m / s scores 2]A1

(b) mention of standing waves or superposition or interferenceB1

mention of two waves, opposite directionsB1

because they are permanently out of phase, permanently destructively interfere, permanently in antiphase

B1[6]

M6. reflection wavefront direction sensible

B1refraction wavefront direction sensible

B1one pair of wavefronts correctly spaced

B1[3]

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M7. (a) (i) 2(.0) × 10–5 m (i.e. allow 1 sf)

B11

(ii) λ = 4(.0) × 10–4 (m)

B1

v = fλ (condone c = fλ)

C1

3.0 MHz sf penalty appliesallow e.c.f. for omitting 10–4 (300 Hz) but sf penaltyapplies for e.g. 0.3 kHz)

A13

(b) (i) ultrasound/wave/pulse/energy spreads out fromthe transmitter (beam not uni-directional)

B1

energy is absorbed by(or lost to) the transmittingmedium/tissue/body

B1

incident ultrasound/wave/pulse/energy is not allreflected (by the reflecting object)

or some is transmitted /absorbed by the organor is reflected at different angles (so does not returnto detector)

B1

some ultrasound/wave/pulse/energy reflected by theskin since gel was not used

B1max2

ANY 2

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(ii) distance travelled 1200 × 95 or 114 000 or 0.114 m(i.e. mark for use of velocity × time ignoring powersof 10)

C1

0.057 m ( allow answers in range 0.055 to 0.057 )

A12

[8]

M8. (a) longitudinal

B1

(b) reflection

B1

(c) use of speed = distance/time

C1

(0.45 or 0.9)/1.6 × 10–4 or 0.45/0.8 × 10–4

C1

= 5.6 km s1 [5.625] A1[5]

M9. use of r2

C1

P = 1.4 × 103 × 4 × 3.14 × (1.5 × 1011)2

C1

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= 3.96 × 1026 W

A1[3]

M10. (a) Good diagram of pressure variations/particle oscillationswith at least one label indicating direction of propagation,pressure variation or density variation

B1

Plus any two from five ofVibrating source

B1

Energy transferred to (air) molecules

B1

Energy passed on by collisions between molecules

B1

Oscillations of air molecule neighbours slightly outof phase

B1

Oscillations/waves are longitudinal/energy transfer parallelto vibrations

B13

(b) Diagram showing several transverse vibrations/waves which aresubsequently limited to one after polarisation

B1

Valid example (light, microwaves etc.)

accept sunlightSuitable polariser for the stated example

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M1

(polaroid, reflection, metal grid etc). Not sunglasses

A13

[6]

M11. (a) Statement that Id2 (or Ir2) should be constant

C1

Calculation of Id2 for two corresponding values of I and d

C1

Calculation of Id2 for three corresponding values of I and dwith conclusion

A13

orwork out constant for one set

C1

Calculate intensity for 1 new distance

C1

Calculate intensity for 2 new distances and compares withgraph.

A1

orReads one value from graph and calculates value for doubledistance

C1

Explains that this is ¼ original intensity

C1

Does this twice with conclusion

A1

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(b) I = P/4πd2 or substitution of two corresponding values of Iand d

C1

0.40 W (condone 1sf)

A12

[5]

M12. (a) longitudinal wave

B11

(b) arrows showing B displaced to the left and C to the right

B11

(c) particles in the transmitting medium are made to vibrate/givenenergy

B1

ormention of a compression/region of increased pressure (orrarefaction)cause nearby particles to vibrate/have energy/move

B1

orthe compression produces a compression further along (themedium)

2[4]

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M13. (a) (i) wavelength read-off = 1.2 mm

B1

(ii) 3200/1.2 × 10-3 ecf from (a) (i)

C13

2.7 MHz

A1

(b) read-off correct 1.3 µs

C1

factor of two correct

C13

= 2.1 × 10-3 m [2.08] c.a.o.

A1[6]

M14.C[1]

M15. amplitude: each point along wave (1)

has same amplitude for progressive wave

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but varies for stationary wave (1)

phase: progressive wave, adjacent points vibrate with different phase (1)

stationary wave, between nodes all particles vibrate in phase[or there are only two phases] (1)

energy transfer: progressive wave, energy is transferred through space (1)stationary wave, energy is not transferred through space (1)

[5]

M16.(a) (i) displacement is distance of particle (1)

from mean [or equilibrium] position (1)

in direction of wave (energy) (1)

amplitude is maximum displacement (1)

wavelength is shortest distance (1)

between two points in phase (1)(max 4)

(b)

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any two points apart (1)(4)

[8]

M17.B[1]

M18.B[1]

M19.(a) time elapsed = 8.5 ± 0.2 (ms) (1) distance travelled = 3 (m) (1) (allow C.E. if d = 1.5 (m))

speed of sound = = 350 m s–1 (353) (1)3

(b) connect oscilloscope across ac source (or diagram or ac to Y plates) (1) adjust time base to give trace (1) adjust voltage sensitivity (1) sinusoidal trace shown (1) how to measure T from trace (1)

max 5

[8]

M20.C[1]

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M21.D[1]

M22.A[1]

M23. B[1]

M24.A[1]

M25.D[1]

M26.B[1]

M27.D[1]

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M28. (a) λ(=2 × 38) = 76(m)

MHz (1)1

(b) (i) angle between cable and horizontal = (1)

T= 110 cos59° = 57N • (56.7N) (1)(allow C.E. for value of angle)

(ii) cross-sectional area (= (2.0 × 10–3)2)

=1.3 × 10–5(m2) (1)(1.26 × 10–5(m2))

stress (1)

= 4.4 × 106Pa (1)(4.38 × 106Pa)(use of 56.7 and 1.26 gives 4.5 × 106 Pa)(allow C.E. for values of T and area)

(iii) breaking stress is 65 × stresscopper is ductilecopper wire could extend much more before breakingbecause of plastic deformationextension to breaking point unlikely

any three (1)(1)(1)7

[8]

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M29. (a) (i) 0.4(0) m (1)

(ii) speed ( = frequency × wavelength) = 22 × 0.4(0) ecf (1)= 8.8 (m s–1) (1)

(ii) 90 or 450 (1) ° or degrees (1)or 0.5π or 2.5π or 5π/2 (1) rad(ians)or r or r (1) no R, Rad, etc

5

(b) displacement of Y will be a positive (or ‘up’) maximum at 1/4 of a period (or cycle) (0.0114 s) (1)

returns to original position (at 0.5 of a period or cycle) (owtte) (1)2

[7]

M30. (a) (i) one ‘loop’ (accept single line only, accept single dashed line)

+ nodes at each bridge (± length of arrowhead)

+ antinode at centre (1)1

(ii) λ0 = 2L or λ = 0.64 × 2 (1)

= 1.3 (m) (1) (1.28)2

(iii) (c = f λ) = 108 × (a)(ii) (1)

= 138 to 140(.4) (m s–1) (1) ecf from (a) (ii)2

(b) (i) four antinodes (1) (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’

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+ middle 3 nodes labelled ‘N’, ‘n’ or ‘node’ (1)2

(ii) (4 f0 =) 430 (Hz) (1) (432)

or use of f = gives 430 to 440 Hz correct answer only, no ecf1

(c) decrease the length/increase tension/tighten string (1)1

[9]

M31. (a) maximum displacement from equilibrium/meanposition/mid-point/etc (1)

1

(b) (i) any one from:

surface of water/water waves/in ripple tank (1)

rope (1)

slinky clearly qualified as transverse (1)

secondary (‘s’) waves (1)max 1

(ii) transverse wave: oscillation (of medium) is perpendicular towave travel

or transverse can be polarised

or all longitudinal require a medium (1)1

(c) (i) vertical line on B ± 5° (1)1

(ii)

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max 0, 180, 360 + min 90, 270 (1)

and line reaches same minimum and maximum every timeand reasonable shape (1)

2

(d) appropriate use (1)

reason for Polaroid filter being used (1)

eg

Polaroid glasses/sunglasses/ to reduce glare windscreens

camera reduce glare/enhance image

(in a) microscope to identify minerals/rocks

polarimeter to analyse chemicals/concentration or type of sugar

stress analysis reveals areas of high/low stress/ other relevant detail

LCD displays very low power/other relevant detail

3D glasses enhance viewing experience, etc2

[8]

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M32. (a) the maximum displacement (of the wave or medium)

from the equilibrium position

accept ‘rest position’, ‘undisturbed position’, ‘mean position’2

(b) (vertically) downwards (¼ cycle to maximum negative displacement)

then upwards (¼ cycle to equilibrium position and ¼ cycle to maximumpositive displacement)

down (¼ cycle) to equilibrium position/zero displacement and correctreference to either maximum positive or negative displacement or correctreference to fractions of the cycle

candidate who correctly describes the motion of a knot 180 degrees out ofphase with the one shown can gain maximum two marks(ie knot initially moving upwards)

3

(c) max 3 from

stationary wave formed

by superposition or interference (of two progressive waves)

knot is at a node

waves (always) cancel where the knot is

allow ‘standing wave’3

[8]

M33. (a) (wave) B

(the parts of the) spring oscillate / move back and forth in direction of / parallelto wave travelORmention of compressions and rarefactions

Second mark can only be scored if first mark is scored2

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

(ii) wave A: arrow vertically upwards

wave B: arrow horizontally to the left 2

(c) (transmitted radio waves are often) polarised

aerial (rods) must be aligned in the same plane (of polarisation / electric field) ofthe wave

2[7]

M34. (a) (i) oscillates / vibrates

(allow goes up and down / side to side / etc, repeatedly, continuously, etc)

about equilibrium position / perpendicularly to central line 2

(ii) X and Y: antiphase / 180 (degrees out of phase) / п (radians out of phase)

X and Z: in phase / zero (degrees) / 2п (radians) 2

(b) (i) v = fλ

= 780 x 0.32 / 2 or 780 x 0.16 OR 780 x 320 / 2 or 780 x 160

THIS IS AN INDEPENDENT MARK

= 124.8 (m s–1) correct 4 sig fig answer must be seen2

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(ii) ¼ cycle

T = 1 / 780 OR = 1.28 × 10–3

0.25 × 1.28 × 10–3

= 3.2 × 10–4 (s)

Allow correct alternative approach using distance of 0.04m

travelled by progressive wave in ¼ cycle divided by speed.

0.04 /125 = 3.2 × 10–4 (s) 3

(c) (i) antinode 1

(ii) 2 x 0.240

= 0.48 m ‘480m’ gets 1 mark out of 22

(iii) (f = v/λ = 124.8 or 125 / 0.48 ) = 260 (Hz) ecf from cii 1

[13]

M35. (a) (i) oscillates / vibrates

(allow goes up and down / side to side / etc, repeatedly, continuously, etc)

about equilibrium position / perpendicularly to central line 2

(ii) X and Y: antiphase / 180 (degrees out of phase) / п (radians out of phase)

X and Z: in phase / zero (degrees) / 2п (radians) 2

Page 53


(b) (i) v = fλ

= 780 x 0.32 / 2 or 780 x 0.16 OR 780 x 320 / 2 or 780 x 160

THIS IS AN INDEPENDENT MARK

= 124.8 (m s–1) correct 4 sig fig answer must be seen2

(ii) ¼ cycle

T = 1 / 780 OR = 1.28 × 10–3

0.25 × 1.28 × 10–3

= 3.2 × 10–4 (s)

Allow correct alternative approach using distance of 0.04m

travelled by progressive wave in ¼ cycle divided by speed.

0.04 /125 = 3.2 × 10–4 (s) 3

(c) (i) antinode 1

(ii) 2 x 0.240

= 0.48 m ‘480m’ gets 1 mark out of 22

(iii) (f = v/λ = 124.8 or 125 / 0.48 ) = 260 (Hz) ecf from cii 1

[13]

Page 54


E3.(a) Many candidates incorrectly gave laser or sodium vapour lamp as a source producing a continuous spectrum.

(b) (i) Many candidates correctly calculated the first angle.

(ii) Many simply doubled the answer to part (i) to calculate the angular dispersion. Use of the sine or tangent was relatively uncommon and even with error carried forward few candidates gained the mark for the width of the first order spectrum.

(c) Most candidates recognised that the intensity would fall because the energy was being spread out over a larger area, many candidates recognised that this was an inverse square relationship but only the strongest calculated the correct factor.

E4.There were many highly competent and successful solutions to this simple question. However, there were many significant figure and unit penalties – all the more surprising since the unit of the answer was mentioned in the question itself.

E5.(a) A simple opening question that was well done by many apart from an extremely common significant penalty deduction. Weaker candidates often did not recall that the sound pulse travels to the wall and back again, thus travelling twice the 18m distance quoted in the question.

(b) This was not well done. Although a substantial number gained 2 out of 3 on a generous mark scheme, only rarely did an answer give any sense that the pattern of maxima and minima was fixed in space. Answers dealt exclusively with the cancellation issues with no real discussion of the permanence of the cancellation of time and space.

E6. Drawings were again very poor. Examiners awarded marks not only for correct directions of the wavefronts but also for an awareness that wavefront spacings change in refraction and remain unchanged in reflection. Candidates really must take more trouble

Page 55


over these relatively simple drawings if they are not to throw away marks.

E7. (a) (i) This was usually completed successfully. A significant proportion gave the answer as 2 s/10–5 m suggesting that they did not understand how axes are labelled.

(ii) This was often correct but many incurred a significant figure penalty in this part. A common error was to ignore the 10–4 on the d axis.

(b) (i) The majority gave at least one correct reason and many were able to give two.

When discussing the fact that energy was absorbed many did not say where this was occurring. Some suggested that energy was used up to transmit the wave through the medium. Some responses seemed to be trying to express the spreading of the energy of the wave and wrote unconvincingly about refraction and diffraction giving insufficient detail.

(ii) There were many correct answers but failure to realise that the pulse has to travel to and from the reflecting object and incorrect powers of 10 lost many candidates a mark.

E8. (a) Many were able to suggest that the wave in the rod is longitudinal.

(b) Too many used the terms ‘echo’ or ‘refraction’ or ‘standing wave’ in their answers and scored zero on this part.

(c) Many candidates failed to recognise that the pulse travels to the end of the rod and back again and thus lost marks by arriving at an answer that was half that required. Even those who negotiated this hurdle frequently scored a significant penalty error.

E9. Although almost all candidates recognised the need to square the Sun–Moon distance, some could go no further and produced muddled and incorrect solutions.Candidates who wrote the relevant formula down clearly and kept their work tidy were

Page 56


usually able to arrive at a convincing and correct answer.

E10. In part (a) diagrams and explanations varied from excellent to non-existent. The best candidates provided a well-labelled diagram of an oscillating source radiating a longitudinal wave in air. They went on to write about the vibrations of the source being passed on to the air molecules around it, and the energy being propagated as the result of collisions between oscillating molecules.

Part (b) was quite often answered well, but some candidates confused polarisation with diffraction and referred to a polarising slit for visible light.

E11. (a) Although many appeared to know how to proceed the presentation of the argument was usually very poor and examiners were frequently left to decipher a random array of figures to ascertain whether this really was the case. The majority thought that taking two points on the graph was adequate to demonstrate the law. Candidates should know that for two points a straight line or any other curve could be drawn so that at least one extra set of points needs to be considered to make a confident assertion that the particular curve illustrates an inverse square law.

(b) There were many correct answers but a common error was a misquote of the

formula as . A significant number of weaker candidates used .

E12. (a) Very few did not know the type of wave although the spelling of longitudinal was often very poor.

(b) This was done very poorly with the majority incorrectly showing displacements of both particles to the right

(c) Most were able to gain at least one mark here and many gained both. Lack of clarity in the response was often the cause of loss of the second mark.

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E13. (a) (i) Only about one-third of candidates were able to make a simple reading from the graph in order to determine the wavelength of the wave.

(ii) Many were able to operate with the equation c = fλ but a large number could not and came to all sorts of grief. Too many used the value for

the speed of an electromagnetic wave, ignoring the value stated in the question.

(b) The question asked for an interpretation of an ultrasound echo experiment and enabled about half of candidates to score full marks. There were cases

where candidates did not remember that an echo requires the sound wave to go to the reflector and back again (a factor of 2), but some were

unable to interpret the graph and settled on inappropriate values for the return time, both through misreads and through misinterpretation of what

was going on.

E15.It was evident that the depth of knowledge necessary to answer this question was not available to the majority of candidates. Even the energy transfer section in

part (c) was the source of wrong or vague or inadequate answers.

E16.In part (a) many candidates struggled with their explanations and often contradicted themselves. Although the question clearly specified a sound wave many

candidates attempted explanations in terms of a transverse wave and they could not transfer their understanding of wavelength to a longitudinal wave. The

rest position of particles was frequently mentioned. Explanations of wavelength showed that the idea of phase is not understood well.

Part (b) gave even the weakest candidates the opportunity to score full marks. λ was almost always correct, but there were some candidates who made the

usual mistakes of 2a. T / 2 and π / 2.

E19.It was pleasing to see that a large number of candidates analysed the oscilloscope trace correctly in part (a) and obtained the correct value for the time elapsing

between the initial pulse and the reflected pulse. There were some errors, as expected, in taking the reading from the trace, some candidates for example,

taking the start of the second pulse as the relevant point, thus giving a total time of 8.0 ms. A significant number of candidates did not realise that the pulse

travelled back to the microphone, i.e. a total distance of 3 m.. This calculation again incurred many significant figure penalties.

The answers to part (b) were, in general, slightly disappointing. The main problem was due to candidates not reading the question properly and

consequently not describing how the source was connected to the oscilloscope (or Y plates). Many candidates did not describe how the oscilloscope was

set up, i.e. adjusting the voltage sensitivity and time base to give a trace, but assumed that this had already been done. Some very neat traces were drawn

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but others were sketched very casually and did not gain the allocated mark. The majority of candidates described correctly how the period of the wave and

hence the frequency was obtained from the trace.

E23. This question was answered correctly by 58% of the candidates. Lack of understanding of radian measure when considering phase difference probably

accounted for 27% of the candidates choosing distractor D (3π/2), rather than π/2.

E28. Most candidates gave a correct frequency calculation in part (a), although unfortunately some made a significant figure error in their final answer.

In part (b) (i), many candidates correctly calculated the angle between cable P and the ground or the mast. Many were then able to calculate the tension

correctly, although some lost the final mark because they mistakenly doubled their answer, presumably on the grounds that the copper wire pulled on each

mast. In part (ii), most candidates knew the correct expression for the stress but a significant number of candidates lost a mark through making an

arithmetical error in the calculation of the cross-sectional area of the wire, or lost the final two marks as a result of using the expression for the surface area

of the wire instead of the cross-sectional area. Other candidates lost the final mark as a result of a unit error in the final answer or an arithmetical error in the

final calculation.

Many candidates scored two marks in part (iii) by comparing the breaking stress with their own calculated value and reaching a valid conclusion. Some

candidates gained these marks by calculating the breaking force and comparing that with the tension in the wire. Very few candidates considered other

relevant points such as the ductile nature of copper.

E29. Most picked up full marks to parts (a) (i) and (ii).

Candidates tended to successfully state the phase difference and the unit to part (iii). A few confused path difference with phase difference and gave an

answer as a number of wavelengths.

Part (b) should have been a fairly easy question, but was quite poorly answered by many candidates. There was much confusion over the meaning of

displacement. Many thought point Y goes down then up. Few stated that a positive peak is reached after ¼ period. Many referred to wavelength rather than

period or think that this is a stationary wave and the ‘node’ would not move. Many believed point Y would move horizontally.

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E30. In part (a) (i), about 60% of candidates drew one ‘loop’ and picked up the mark. However, we were fairly lenient on the shape of the ‘loop’ and students

need to practice drawing these shapes.

Part (a) (ii) was expected to be a little easier than it was. 42% scored no marks on this despite the benefit of an error carried forward from an incorrect part

(a) (i). Many did not realise the wavelength was found from the length of the string and knowledge of the shape of the fundamental. Some candidates used λ

= v/f with v = speed of light. In contrast, most candidates found part (a) (iii) a very easy calculation.

The majority of candidates got four antinodes in part (b) (i), but then nearly half of those lost the second mark by either not sketching the curve carefully

enough or, more commonly, forgetting to label the antinodes.

In part (c), the vast majority correctly suggested tightening or shortening the string. A few thought that plucking harder would increase the pitch and some

suggested increasing the length, using a thinner string, increasing the wave speed, or even ‘play faster’.

E31. In part (a), the strict definition of amplitude was expected. Candidates needed to say ‘maximum displacement’ and then indicate in some way that this was

relative to the equilibrium position.

The majority, however, chose to define amplitude as the distance between the centre and the peak.

For part (b) (i), the majority of candidates could not give an example of a transverse wave other than electromagnetic waves. Most gave a form of

electromagnetic radiation (most commonly ‘light’) or even sound. Common answers that were accepted included ‘water waves’, ‘waves on strings’ or ‘s-

waves’.

Most candidates realised that a comparison between the direction of wave travel and the oscillation of the medium was a good way to answer part (b) (ii). It

was common, however, for candidates to struggle to express this clearly. The most common error was to say that a transverse wave ‘moves’ perpendicular

to the direction of wave travel rather than ‘oscillation is perpendicular to direction of wave travel’.

The vast majority of candidates found part (c) (ii) very straight forward.

The majority of candidates had no problem with part (c) (ii). The exact shape of the line was not important as long as the maximum and minimum intensities

appeared in the right place.

There were many very good answers to part (d), such as ‘sunglasses/ski goggles reduce glare from light reflected from water/snow’ and ‘a camera filter

reduces unwanted reflections’. Common inadequate responses included saying that polarising sunglasses ‘reduce light intensity’ because the lenses are

‘darker’, or that polarising filters reduce UV.

E32. Many students had learned the correct definition in part (a) but some gave a description, for example ‘the greatest height of the wave from the middle’. This

did not gain marks.

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Surprisingly in answer to part (b), many students referred to the equilibrium position as the ‘node’ and maximum amplitude as the ‘antinode’ on a

progressive wave. Many use fractions of a cycle to describe the position of the knot but some use angles or fractions of a wavelength which are not

appropriate. The biggest loss of marks occurred in the first mark where a large number thought that the knot would be travelling upwards initially.

Part (c) was a fairly easy question with students only needing to state that the ‘knot is at a node on a stationary wave which is caused by superposition’ to

get three marks. Most students managed to get two of the marking points. Many did not understand how a node is formed, believing it is the sum of a peak

and a trough only, or that the whole rope is stationary, or that the rope is only stationary at a node when cancellation occurs between waves that are 180°

out of phase. The two waves that form a stationary wave are not always 180° out of phase in order to cancel at the nodes. Nodes are where the wave

always cancels but the phase difference between the waves repeatedly varies from zero to 2π. Cancellation everywhere on the stationary wave only occurs

when the waves are in antiphase but cancellation always happens at the nodes because the displacements of the waves are always equal and opposite at

those points (or displacements are both zero when in phase and in antiphase). This is a complex situation but there are many simulations available on the

internet that help to get these ideas across.

E33. Most did well in part (b)(i) and indicated a complete wavelength very precisely, though a generous tolerance was allowed. A significant number thought the

coils constituted the waveform and gave the spacing between one or two coils as the wavelength and some chose the compression or the rarefaction or the

whole length of the spring. In part (b)(ii) many believed point P would move downwards. This is a very common misconception and a similar question has

appeared in a past paper. The behaviour of point Q is more difficult to understand. The particle changes direction when the centre of a rarefaction or

compression reaches it. If the wave is moving to the right, then as the compression gets closer to the particle, the particle will move left towards the

compression.

In (c) the majority of students surprisingly did not recognise that this was about polarisation. Those who did point this out did not describe the aerial being

aligned with the plane of polarisation.

E34. Part (a)(i) was almost universally misinterpreted due to a similar question appearing on a previous paper. Many students interpreted the question as

‘describe the motion over the next cycle’. Those who did this often failed to point out that there was a continuing oscillation taking place. Part (a)(ii) was very

poorly answered which was a surprise. A common answer was ‘out of phase’ for X and Y which is not equivalent to ‘antiphase’. Phase was often given in

terms of number of wavelengths, e.g. ½λ. There was little understanding of the difference between phase difference along a progressive wave and a

stationary wave. Many had measured the fraction of a wavelength between the points and converted this into an angle as you would for a progressive wave.

It is suggested that phase difference along a stationary wave be demonstrated by referring to the many simulations available.

Part (b)(i) presented few problems for students. In part (b)(ii) many students did 1/780 and obtained the time for one complete cycle but did not recognise

that they needed to divide by 4 to get the time for ¼ of a cycle. A significant number thought that the time between maximum displacement and reaching the

equilibrium position was half a cycle. Some divided 780 by 4 which makes the answer 8 times greater than it should be.

For part (c)(i) most students got ‘antinode’ but a significant number put ‘node’/ ‘amplitude’/ ‘max displacement’ / ‘stationary wave’ / ‘equilibrium’ / ‘maxima’.

Part (c)(ii) presented few problems for students. In part (c)(iii) quite a few students left this blank because they were unable to answer the previous question.

However, many of those who scored the mark did so by using an incorrect answer to (c)(ii). Students should be encouraged not to give up; the final part of a

question is not necessarily the hardest.

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E35. Part (a)(i) was almost universally misinterpreted due to a similar question appearing on a previous paper. Many students interpreted the question as

‘describe the motion over the next cycle’. Those who did this often failed to point out that there was a continuing oscillation taking place. Part (a)(ii) was very

poorly answered which was a surprise. A common answer was ‘out of phase’ for X and Y which is not equivalent to ‘antiphase’. Phase was often given in

terms of number of wavelengths, e.g. ½λ. There was little understanding of the difference between phase difference along a progressive wave and a

stationary wave. Many had measured the fraction of a wavelength between the points and converted this into an angle as you would for a progressive wave.

It is suggested that phase difference along a stationary wave be demonstrated by referring to the many simulations available.

Part (b)(i) presented few problems for students. In part (b)(ii) many students did 1/780 and obtained the time for one complete cycle but did not recognise

that they needed to divide by 4 to get the time for ¼ of a cycle. A significant number thought that the time between maximum displacement and reaching the

equilibrium position was half a cycle. Some divided 780 by 4 which makes the answer 8 times greater than it should be.

For part (c)(i) most students got ‘antinode’ but a significant number put ‘node’/ ‘amplitude’/ ‘max displacement’ / ‘stationary wave’ / ‘equilibrium’ / ‘maxima’.

Part (c)(ii) presented few problems for students. In part (c)(iii) quite a few students left this blank because they were unable to answer the previous question.

However, many of those who scored the mark did so by using an incorrect answer to (c)(ii). Students should be encouraged not to give up; the final part of a

question is not necessarily the hardest.

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Documents

· Web viewThe diagram below shows a hammer being struck against the end of a horizontal metal rod. A pulse of sound travels along the rod from where the hammer strikes it to the