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Waves revision [116 marks]
1. A first-harmonic standing wave is formed on a vertical string of length 3.0 m using avibration generator. The boundary conditions for this string are that it is fixed at oneboundary and free at the other boundary.
The generator vibrates at a frequency of 300 Hz.
What is the speed of the wave on the string?
A. 0.90 km s
B. 1.2 km s
C. 1.8 km s
D. 3.6 km s
MarkschemeD
Examiners report[N/A]
–1
–1
–1
–1
Two travelling waves are moving through a medium. The diagram shows, for a point in
[1 mark]
2. Two travelling waves are moving through a medium. The diagram shows, for a point inthe medium, the variation with time t of the displacement d of each of the waves.
For the instant when t = 2.0 ms, what is the phase difference between the waves and what isthe resultant displacement of the waves?
MarkschemeD
Examiners report[N/A]
3. The diagram shows an interference pattern produced by two sources that oscillate onthe surface of a liquid.
Which of the distances shown in the diagram corresponds to one fringe width of the interferencepattern?
MarkschemeC
[1 mark]
[1 mark]
Examiners report[N/A]
4. A system that is subject to a restoring force oscillates about an equilibrium position.
For the motion to be simple harmonic, the restoring force must be proportional to
A. the amplitude of the oscillation.
B. the displacement from the equilibrium position.
C. the potential energy of the system.
D. the period of the oscillation.
MarkschemeB
Examiners report[N/A]
5. A particle is displaced from rest and released at time t = 0. It performs simple harmonicmotion (SHM). Which graph shows the variation with time of the kinetic energy E of theparticle?
MarkschemeD
k
[1 mark]
[1 mark]
Examiners report[N/A]
6. Two sound waves from a point source on the ground travel through the ground to adetector. The speed of one wave is 7.5 km s , the speed of the other wave is 5.0 km s. The waves arrive at the detector 15 s apart. What is the distance from the point source to the
detector?
A. 38 km
B. 45 km
C. 113 km
D. 225 km
MarkschemeD
Examiners report[N/A]
–1 –
1
7. What is true about the acceleration of a particle that is oscillating with simple harmonicmotion (SHM)?
A. It is in the opposite direction to its velocity
B. It is decreasing when the potential energy is increasing
C. It is proportional to the frequency of the oscillation
D. It is at a minimum when the velocity is at a maximum
MarkschemeD
Examiners report[N/A]
What are the changes in the speed and in the wavelength of monochromatic light when
[1 mark]
[1 mark]
8. What are the changes in the speed and in the wavelength of monochromatic light whenthe light passes from water to air?
MarkschemeA
Examiners report[N/A]
9. A sound wave has a wavelength of 0.20 m. What is the phase difference between twopoints along the wave which are 0.85 m apart?
A. zero
B. 45°
C. 90°
D. 180°
MarkschemeC
Examiners report[N/A]
10. A pair of slits in a double slit experiment are illuminated with monochromatic lightof wavelength 480 nm. The slits are separated by 1.0 mm. What is the separation ofthe fringes when observed at a distance of 2.0 m from the slits?
A. 2.4 × 10 mm
B. 9.6 × 10 mm
C. 2.4 × 10 mm
D. 9.6 × 10 mm
–4
–4
–1
–1
[1 mark]
[1 mark]
[1 mark]
MarkschemeD
Examiners report[N/A]
11. A ray of light passes from the air into a long glass plate of refractive index n at an angleθ to the edge of the plate.
The ray is incident on the internal surface of the glass plate and the refracted ray travels alongthe external surface of the plate.
What change to n and what change to θ will cause the ray to travel entirely within the plate afterincidence?
MarkschemeA
Examiners report[N/A]
A string stretched between two fixed points sounds its second harmonic at frequency f.
[1 mark]
12. A string stretched between two fixed points sounds its second harmonic at frequency f.
Which expression, where n is an integer, gives the frequencies of harmonics that have a nodeat the centre of the string?
A.
B. nf
C. 2nf
D. (2n + 1)f
MarkschemeB
Examiners report[N/A]
fn+12
13a.
A beam of coherent monochromatic light from a distant galaxy is used in an optics experimenton Earth.
The beam is incident normally on a double slit. The distance between the slits is 0.300 mm. Ascreen is at a distance D from the slits. The diffraction angle θ is labelled.
A series of dark and bright fringes appears on the screen. Explain how a dark fringe isformed.
[1 mark]
[3 marks]
Markschemesuperposition of light from each slit / interference of light from both slits
with path/phase difference of any half-odd multiple of wavelength/any odd multiple of (inwords or symbols)
producing destructive interference
Ignore any reference to crests and troughs.
[3 marks]
Examiners report[N/A]
π
13b. The wavelength of the beam as observed on Earth is 633.0 nm. The separationbetween a dark and a bright fringe on the screen is 4.50 mm. Calculate D.
Markschemeevidence of solving for D «D = »
« × 2» = 4.27 «m»
Award [1] max for 2.13 m.
[2 marks]
Examiners report[N/A]
sdλ
4.50×10−3×0.300×10−3
633.0×10−9
The air between the slits and the screen is replaced with water. The refractive index of water is
[2 marks]
13c.
The air between the slits and the screen is replaced with water. The refractive index of water is1.33.
Calculate the wavelength of the light in water.
Markscheme = 476 «nm»
[1 mark]
Examiners report[N/A]
633.01.33
13d. State two ways in which the intensity pattern on the screen changes.
Markschemedistance between peaks decreases
intensity decreases
[2 marks]
Examiners report[N/A]
A loudspeaker emits sound towards the open end of a pipe. The other end is closed. A standing
[1 mark]
[2 marks]
14a.
A loudspeaker emits sound towards the open end of a pipe. The other end is closed. A standingwave is formed in the pipe. The diagram represents the displacement of molecules of air in thepipe at an instant of time.
Outline how the standing wave is formed.
Markschemethe incident wave «from the speaker» and the reflected wave «from the closed end»
superpose/combine/interfere
Allow superimpose/add up
Do not allow meet/interact
[1 mark]
Examiners report[N/A]
14b.
X and Y represent the equilibrium positions of two air molecules in the pipe. The arrowrepresents the velocity of the molecule at Y.
Draw an arrow on the diagram to represent the direction of motion of the molecule at X.
MarkschemeHorizontal arrow from X to the right
MP2 is dependent on MP1
Ignore length of arrow
[1 mark]
[1 mark]
[1 mark]
Examiners report[N/A]
14c. Label a position N that is a node of the standing wave.
MarkschemeP at a node
[1 mark]
Examiners report[N/A]
14d. The speed of sound is 340 m s and the length of the pipe is 0.30 m. Calculate, in Hz,the frequency of the sound.
Markschemewavelength is λ = « =» 0.40 «m»
f = « » 850 «Hz»
Award [2] for a bald correct answer
Allow ECF from MP1
[2 marks]
–1
4×0.303
3400.40
[1 mark]
[2 marks]
Examiners report[N/A]
14e.
The loudspeaker in (a) now emits sound towards an air–water boundary. A, B and C are parallelwavefronts emitted by the loudspeaker. The parts of wavefronts A and B in water are not shown.Wavefront C has not yet entered the water.
The speed of sound in air is 340 m s and in water it is 1500 m s .
The wavefronts make an angle θ with the surface of the water. Determine the maximum angle,θ , at which the sound can enter water. Give your answer to the correct number of significantfigures.
–1 –1
max
[2 marks]
Markscheme
θ = 13«°»
Award [2] for a bald correct answer
Award [2] for a bald answer of 13.1
Answer must be to 2/3 significant figures to award MP2
Allow 0.23 radians
[2 marks]
Examiners report[N/A]
=sin θc
3401
1500
c
14f. Draw lines on the diagram to complete wavefronts A and B in water for θ < θ .
Markschemecorrect orientation
greater separation
Do not penalize the lengths of A and B in the water
Do not penalize a wavefront for C if it is consistent with A and B
MP1 must be awarded for MP2 to be awarded
[2 marks]
Examiners report[N/A]
max
A series of dark and bright fringes appears on the screen. Explain how a dark fringe is
[2 marks]
15a. A series of dark and bright fringes appears on the screen. Explain how a dark fringe isformed.
Markschemesuperposition of light from each slit / interference of light from both slits
with path/phase difference of any half-odd multiple of wavelength/any odd multiple of (inwords or symbols)
producing destructive interference
Ignore any reference to crests and troughs.
[3 marks]
Examiners report[N/A]
π
A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment
[3 marks]
15b.
A beam of coherent monochromatic light from a distant galaxy is used in an optics experimenton Earth.
The beam is incident normally on a double slit. The distance between the slits is 0.300 mm. Ascreen is at a distance D from the slits. The diffraction angle θ is labelled.
Outline why the beam has to be coherent in order for the fringes to be visible.
Markschemelight waves (from slits) must have constant phase difference / no phase difference / be inphase
OWTTE
[1 mark]
Examiners report[N/A]
The graph of variation of intensity with diffraction angle for this experiment is shown.
[1 mark]
15c.
The graph of variation of intensity with diffraction angle for this experiment is shown.
Calculate the angular separation between the central peak and the missing peak in thedouble-slit interference intensity pattern. State your answer to an appropriate numberof significant figures.
Markschemesin θ =
sin θ = 0.0084401…
final answer to three sig figs ( eg 0.00844 or 8.44 × 10 )
Allow ECF from (a)(iii).
Award [1] for 0.121 rad (can award MP3 in addition for proper sig fig)
Accept calculation in degrees leading to 0.481 degrees.
Award MP3 for any answer expressed to 3sf.
[3 marks]
Examiners report[N/A]
4×633.0×10−9
0.300×10−3
–3
Deduce, in mm, the width of one slit.
[3 marks]
15d. Deduce, in mm, the width of one slit.
Markschemeuse of diffraction formula «b =
»
OR
«=» 7.5«00» × 10 «mm»
Allow ECF from (b)(i).
[2 marks]
Examiners report[N/A]
λθ
633.0×10−9
0.00844
–2
15e. The wavelength of the light in the beam when emitted by the galaxy was 621.4 nm.
Explain, without further calculation, what can be deduced about the relative motion of the galaxyand the Earth.
[2 marks]
[2 marks]
Markschemewavelength increases (so frequency decreases) / light is redshifted
galaxy is moving away from Earth
Allow ECF for MP2 (ie wavelength decreases so moving towards).
[2 marks]
Examiners report[N/A]
16a.
A small ball of mass m is moving in a horizontal circle on the inside surface of a frictionlesshemispherical bowl.
The normal reaction force N makes an angle θ to the horizontal.
State the direction of the resultant force on the ball.
Markschemetowards the centre «of the circle» / horizontally to the right
Do not accept towards the centre of the bowl
[1 mark]
Examiners report[N/A]
On the diagram, construct an arrow of the correct length to represent the weight of the
[1 mark]
16b. On the diagram, construct an arrow of the correct length to represent the weight of theball.
Markschemedownward vertical arrow of any length
arrow of correct length
Judge the length of the vertical arrow by eye. The construction lines are not required. Alabel is not required
eg:
[2 marks]
Examiners report[N/A]
Show that the magnitude of the net force F on the ball is given by the
[2 marks]
16c. Show that the magnitude of the net force F on the ball is given by thefollowing equation.
MarkschemeALTERNATIVE 1
F = N cos θmg = N sin θdividing/substituting to get result
ALTERNATIVE 2
right angle triangle drawn with F, N and W/mg labelled
angle correctly labelled and arrows on forces in correct directions
correct use of trigonometry leading to the required relationship
tan θ =
[3 marks]
Examiners report[N/A]
F =mg
tan θ
=OA
mg
F
The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.
[3 marks]
16d. The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.
Markscheme = m
r = R cos θ
v =
v = 13.4/13 «ms »
Award [4] for a bald correct answer
Award [3] for an answer of 13.9/14 «ms ». MP2 omitted
[4 marks]
Examiners report[N/A]
mg
tanθ
v2
r
√ /√ /√gRcos2θ
sin θ
gRcosθ
tanθ9.81×8.0cos22
tan22
–1
–1
Outline whether this ball can move on a horizontal circular path of radius equal to
[4 marks]
16e. Outline whether this ball can move on a horizontal circular path of radius equal tothe radius of the bowl.
Markschemethere is no force to balance the weight/N is horizontal
so no / it is not possible
Must see correct justification to award MP2
[2 marks]
Examiners report[N/A]
The ball is now displaced through a small distance x from the bottom of the bowl and is then
[2 marks]
16f.
The ball is now displaced through a small distance x from the bottom of the bowl and is thenreleased from rest.
The magnitude of the force on the ball towards the equilibrium position is given by
where R is the radius of the bowl.
Outline why the ball will perform simple harmonic oscillations about the equilibriumposition.
Markschemethe «restoring» force/acceleration is proportional to displacement
Direction is not required
[1 mark]
Examiners report[N/A]
mgx
R
16g. Show that the period of oscillation of the ball is about 6 s.
[1 mark]
[2 marks]
Markschemeω = «
» = «= 1.107 s »
T = « =
=» 5.7 «s»
Allow use of or g = 9.8 or 10
Award [0] for a substitution into T = 2π
[2 marks]
Examiners report[N/A]
√ g
R√ 9.81
8.0–1
2πω2π
1.107
√ Ig
16h. The amplitude of oscillation is 0.12 m. On the axes, draw a graph to show the variationwith time t of the velocity v of the ball during one period.
[3 marks]
Markschemesine graph
correct amplitude «0.13 m s »
correct period and only 1 period shown
Accept ± sine for shape of the graph. Accept 5.7 s or 6.0 s for the correct period.
Amplitude should be correct to ± square for MP2
eg: v /m s
[3 marks]
Examiners report[N/A]
–1
12
–1
17a. Outline how the standing wave is formed.
Markschemethe incident wave «from the speaker» and the reflected wave «from the closed end»
superpose/combine/interfere
Allow superimpose/add up
Do not allow meet/interact
[1 mark]
Examiners report[N/A]
17b. Draw an arrow on the diagram to represent the direction of motion of the molecule at X.
[1 mark]
[1 mark]
MarkschemeHorizontal arrow from X to the right
MP2 is dependent on MP1
Ignore length of arrow
[1 mark]
Examiners report[N/A]
17c. Label a position N that is a node of the standing wave.
MarkschemeP at a node
[1 mark]
Examiners report[N/A]
17d. The speed of sound is 340 m s and the length of the pipe is 0.30 m. Calculate, in Hz,the frequency of the sound.
–1
[1 mark]
[2 marks]
Markschemewavelength is λ = « =» 0.40 «m»
f = « » 850 «Hz»
Award [2] for a bald correct answer
Allow ECF from MP1
[2 marks]
Examiners report[N/A]
4×0.303
3400.40
17e. The speed of sound in air is 340 m s and in water it is 1500 m s .
The wavefronts make an angle θ with the surface of the water. Determine the maximum angle,θ , at which the sound can enter water. Give your answer to the correct number of significantfigures.
Markscheme
θ = 13«°»
Award [2] for a bald correct answer
Award [2] for a bald answer of 13.1
Answer must be to 2/3 significant figures to award MP2
Allow 0.23 radians
[2 marks]
–1 –1
max
=sin θc
3401
1500
c
[2 marks]
Examiners report[N/A]
17f. Draw lines on the diagram to complete wavefronts A and B in water for θ < θ .
Markschemecorrect orientation
greater separation
Do not penalize the lengths of A and B in the water
Do not penalize a wavefront for C if it is consistent with A and B
MP1 must be awarded for MP2 to be awarded
[2 marks]
Examiners report[N/A]
max
18. The graph shows the variation with time t of the velocity v of an objectundergoing simple harmonic motion (SHM). At which velocity does the displacementfrom the mean position take a maximum positive value?
MarkschemeD
[2 marks]
[1 mark]
Examiners report[N/A]
19. What is the phase difference, in rad, between the centre of a compression and thecentre of a rarefaction for a longitudinal travelling wave?
A. 0
B.
C.
D.
MarkschemeC
Examiners report[N/A]
π2
π
2π
20. Two wave pulses, each of amplitude A, approach each other. They then superposebefore continuing in their original directions. What is the total amplitude duringsuperposition and the amplitudes of the individual pulses after superposition?
MarkschemeD
[1 mark]
[1 mark]
Examiners report[N/A]
21. The refractive index for light travelling from medium X to medium Y is . The refractive
index for light travelling from medium Y to medium Z is . What is the refractive index for lighttravelling from medium X to medium Z?
A.
B.
C.
D.
MarkschemeA
Examiners report[N/A]
43
35
45
1512
54
2915
22. A pipe of fixed length is closed at one end. What is ?
A.
B.
C. 3
D. 5
MarkschemeC
Examiners report[N/A]
third harmonic frequency of pipefirst harmonic frequency of pipe
15
13
The graph shows the variation with position s of the displacement x of a wave
[1 mark]
[1 mark]
23. The graph shows the variation with position s of the displacement x of a waveundergoing simple harmonic motion (SHM).
What is the magnitude of the velocity at the displacements X, Y and Z?
MarkschemeB
Examiners report[N/A]
24. The diagram shows a second harmonic standing wave on a string fixed at both ends.
What is the phase difference, in rad, between the particle at X and the particle at Y?
A. 0
B.
C.
D.
MarkschemeA
π4π2
3π
4
[1 mark]
[1 mark]
Examiners report[N/A]
25a.
A large cube is formed from ice. A light ray is incident from a vacuum at an angle of 46˚ to thenormal on one surface of the cube. The light ray is parallel to the plane of one of the sides of thecube. The angle of refraction inside the cube is 33˚.
Calculate the speed of light inside the ice cube.
Markscheme«v = c =»
2.3 x 10 «m s »
Examiners report[N/A]
sin isin r
3×108×sin(33)sin(46)
8 –1
Show that no light emerges from side AB.
[2 marks]
25b. Show that no light emerges from side AB.
Markschemelight strikes AB at an angle of 57°
critical angle is «sin =» 50.1°
49.2° from unrounded value
angle of incidence is greater than critical angle so total internal reflection
OR
light strikes AB at an angle of 57°
calculation showing sin of “refracted angle” = 1.1
statement that since 1.1>1 the angle does not exist and the light does not emerge
[Max 3 marks]
Examiners report[N/A]
–1( )2.33
25c. Sketch, on the diagram, the subsequent path of the light ray.
Markschemetotal internal reflection shown
ray emerges at opposite face to incidence
Judge angle of incidence=angle of reflection by eye or accept correctly labelled angles
With sensible refraction in correct direction
Examiners report[N/A]
[3 marks]
[2 marks]
25d.
Each side of the ice cube is 0.75 m in length. The initial temperature of the ice cube is –20 °C.
Determine the energy required to melt all of the ice from –20 °C to water ata temperature of 0 °C.
Specific latent heat of fusion of ice = 330 kJ kgSpecific heat capacity of ice = 2.1 kJ kg kDensity of ice = 920 kg m
Markschememass = «volume x density» (0.75) x 920 «= 388 kg»
energy required to raise temperature = 388 x 2100 x 20 «= 1.63 x 10 J»
energy required to melt = 388 x 330 x 10 «= 1.28 x 10 J»
1.4 x 10 «J» OR 1.4 x 10 «kJ»
Accept any consistent units
Award [3 max] for answer which uses density as 1000 kg (1.5× 10 «J»)
Examiners report[N/A]
–1
–1 –1
–3
3
7
3 8
8 5
–3 8
Outline the difference between the molecular structure of a solid and a liquid.
[4 marks]
25e. Outline the difference between the molecular structure of a solid and a liquid.
Markschemein solid state, nearest neighbour molecules cannot exchange places/have fixedpositions/are closer to each other/have regular pattern/have stronger forces of attraction
in liquid, bonds between molecules can be broken and re-form
OWTTE
Accept converse argument for liquids
[Max 1 Mark]
Examiners report[N/A]
A particle undergoes simple harmonic motion (SHM). The graph shows the variation of
[1 mark]
26. A particle undergoes simple harmonic motion (SHM). The graph shows the variation ofvelocity v of the particle with time t.
What is the variation with time of the acceleration a of the particle?
MarkschemeA
Examiners report[N/A]
27. What statement about X-rays and ultraviolet radiation is correct?
A. X-rays travel faster in a vacuum than ultraviolet waves.
B. X-rays have a higher frequency than ultraviolet waves.
C. X-rays cannot be diffracted unlike ultraviolet waves.
D. Microwaves lie between X-rays and ultraviolet in the electromagnetic spectrum.
MarkschemeB
[1 mark]
[1 mark]
Examiners report[N/A]
28. Two pulses are travelling towards each other.
What is a possible pulse shape when the pulses overlap?
MarkschemeA
Examiners report[N/A]
Unpolarized light of intensity I is incident on the first of two polarizing sheets. Initially
[1 mark]
29. Unpolarized light of intensity I is incident on the first of two polarizing sheets. Initiallythe planes of polarization of the sheets are perpendicular.
Which sheet must be rotated and by what angle so that light of intensity can emerge fromthe second sheet?
MarkschemeC
Examiners report[N/A]
0
I0
4
30. When a sound wave travels from a region of hot air to a region of cold air, it refracts asshown.
What changes occur in the frequency and wavelength of the sound as it passes from the hot airto the cold air?
[1 mark]
[1 mark]
MarkschemeB
Examiners report[N/A]
31. In simple harmonic oscillations which two quantities always have opposite directions?
A. Kinetic energy and potential energy
B. Velocity and acceleration
C. Velocity and displacement
D. Acceleration and displacement
MarkschemeD
Examiners report[N/A]
32. A girl in a stationary boat observes that 10 wave crests pass the boat every minute.What is the period of the water waves?
A. min
B. min
C. 10 min
D. 10 min
MarkschemeA
Examiners report[N/A]
110
110
–1
–1
The graph shows the variation with distance x of the displacement of the particles of a
[1 mark]
[1 mark]
33. The graph shows the variation with distance x of the displacement of the particles of amedium in which a longitudinal wave is travelling from left to right. Displacements to theright of equilibrium positions are positive.
Which point is at the centre of a compression?
A. x = 0
B. x = 1 m
C. x = 2 m
D. x = 3 m
MarkschemeB
Examiners report[N/A]
34. A beam of unpolarized light is incident on the first of two parallel polarizers. Thetransmission axes of the two polarizers are initially parallel.
The first polarizer is now rotated about the direction of the incident beam by an anglesmaller than 90°. Which gives the changes, if any, in the intensity and polarization of thetransmitted light?
[1 mark]
[1 mark]
MarkschemeA
Examiners report[N/A]
35. The frequency of the first harmonic standing wave in a pipe that is open at both ends is200 Hz. What is the frequency of the first harmonic in a pipe of the same length that isopen at one end and closed at the other?
A. 50 Hz
B. 75 Hz
C. 100 Hz
D. 400 Hz
MarkschemeC
Examiners report[N/A]
36. A travelling wave of period 5.0 ms travels along a stretched string at a speed of 40 m s. Two points on the string are 0.050 m apart.
What is the phase difference between the two points?
A. 0
B.
C.
D. 2
MarkschemeB
Examiners report[N/A]
–
1
π2
π
π
[1 mark]
[1 mark]
37. Properties of waves are
I. polarizationII. diffractionIII. refraction
Which of these properties apply to sound waves?
A. I and IIB. I and IIIC. II and IIID. I, II and III
MarkschemeC
Examiners report[N/A]
38. Water is draining from a vertical tube that was initially full. A vibrating tuning fork is heldnear the top of the tube. For two positions of the water surface only, the sound is at itsmaximum loudness.
The distance between the two positions of maximum loudness is x.
What is the wavelength of the sound emitted by the tuning fork?
A.
B. x
C.
D. 2x
MarkschemeD
x2
3x
2
[1 mark]
[1 mark]
Examiners report[N/A]
39a. Outline what is meant by the principle of superposition of waves.
Markschemewhen 2 waves meet the resultant displacement
is the «vector» sum of their individual displacements
Displacement should be mentioned at least once in MP 1 or 2.
Examiners report[N/A]
Red laser light is incident on a double slit with a slit separation of 0.35 mm.
[2 marks]
39b. Red laser light is incident on a double slit with a slit separation of 0.35 mm.A double-slit interference pattern is observed on a screen 2.4 m from the slits.The distance between successive maxima on the screen is 4.7 mm.
Calculate the wavelength of the light. Give your answer to an appropriate number of significantfigures.
Markschemeλ =
= 6.9 x 10 «m»
answer to 2 SF
Allow missed powers of 10 for MP1.
Examiners report[N/A]
4.7×10−3×0.35×10−3
2.4
–7
Explain the change to the appearance of the interference pattern when the red-light
[3 marks]
39c. Explain the change to the appearance of the interference pattern when the red-lightlaser is replaced by one that emits green light.
Markschemegreen wavelength smaller than red
fringe separation / distance between maxima decreases
Allow ECF from MP1.
Examiners report[N/A]
39d. One of the slits is now covered.
Describe the appearance of the pattern on the screen.
[2 marks]
[2 marks]
Markschemebright central maximum
subsidiary maxima «on either side»
the width of the central fringe is twice / larger than the width of the subsidiary/secondaryfringes/maxima
OR
intensity of pattern is decreased
Allow marks from a suitably labelled intensity graph for single slit diffraction.
Examiners report[N/A]
A student investigates how light can be used to measure the speed of a toy train.
40a.
A student investigates how light can be used to measure the speed of a toy train.
Light from a laser is incident on a double slit. The light from the slits is detected by a lightsensor attached to the train.
The graph shows the variation with time of the output voltage from the light sensor as the trainmoves parallel to the slits. The output voltage is proportional to the intensity of light incident onthe sensor.
Explain, with reference to the light passing through the slits, why a series of voltagepeaks occurs.
[3 marks]
Markscheme«light» superposes/interferes
pattern consists of «intensity» maxima and minimaORconsisting of constructive and destructive «interference»
voltage peaks correspond to interference maxima
Examiners report[N/A]
40b. The slits are separated by 1.5 mm and the laser light has a wavelength of 6.3 x 10 m.The slits are 5.0 m from the train track. Calculate the separation between two adjacentpositions of the train when the output voltage is at a maximum.
Markscheme« » 2.1 x 10 «m»
If no unit assume m.Correct answer only.
Examiners report[N/A]
–7
s = = =λDd
6.3×10−7×5.01.5×10−3
–3
Estimate the speed of the train.
[1 mark]
40c. Estimate the speed of the train.
Markschemecorrect read-off from graph of 25 m s
v = « » 8.4 x 10 «m s »
Allow ECF from (b)(i)
Examiners report[N/A]
= =xt
2.1×10−3
25×10−3–2 –1
40d. In another experiment the student replaces the light sensor with a sound sensor. Thetrain travels away from a loudspeaker that is emitting sound waves ofconstant amplitude and frequency towards a reflecting barrier.
The sound sensor gives a graph of the variation of output voltage with time along the track thatis similar in shape to the graph shown in the resource. Explain how this effect arises.
[2 marks]
[2 marks]
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MarkschemeALTERNATIVE 1
«reflection at barrier» leads to two waves travelling in opposite directions
mention of formation of standing wave
maximum corresponds to antinode/maximum displacement «of air molecules»ORcomplete cancellation at node position
Examiners report[N/A]