References only, not question text. Open Official paper ↗ where Cambridge publishes the paper,
or see the official Cambridge past-papers page; for other papers, ask your
school. “Paper 42” means Paper 4, variant 2.
Practice questions
Original questions written by HomiLabs in the style of the exam, with answers and mark schemes. They are not
Cambridge past paper questions and have not been reviewed by Cambridge. Try each one before opening the answer.
Q1Progressive waves (phase, intensity, CRO) · Core · Paper 2 style · 5 marks
Ripples on the surface of a fish pond in Faisalabad have a frequency of 2.5 Hz and a wavelength of 0.84 m.
(a)Define the frequency of a wave.[1]
(b)Use the definitions of speed, frequency and wavelength to show that v = fλ.[2]
(c)Calculate the speed of the waves and their period.[2]
Show answer
(a) The number of oscillations (wavelengths passing a point) per unit time.
B1
(b) In one period T the wave travels one wavelength λ, so v = λ/T, and f = 1/T gives v = fλ.
M1 distance λ in time T; A1 f = 1/T leading to v = fλ
(c) v = 2.1 m s⁻¹; T = 0.40 s
v = 2.5 × 0.84 = 2.1 m s⁻¹ (B1); T = 1/2.5 = 0.40 s (B1)
Q2Progressive waves (phase, intensity, CRO) · Core · Paper 1 style · 1 mark
(a)Two points on a progressive wave of wavelength 1.20 m are 0.30 m apart along the direction of travel. What is the phase difference between the oscillations of the two points?[1]
Show answer
(a) B 90°
Phase difference = (0.30/1.20) × 360° = 90°. 180° would need a separation of half a wavelength (0.60 m).
Q3Progressive waves (phase, intensity, CRO) · Core · Paper 2 style · 4 marks
(a)State what is meant by a progressive wave.[1]
(b)Explain the meaning of(i) displacement, (ii) amplitude, (iii) phase difference.[3]
Show answer
(a) A wave that transfers energy from one place to another (without transferring matter).
B1
(b) (i) distance (in a given direction) of a point from its equilibrium position; (ii) maximum displacement; (iii) the fraction of a cycle (in degrees or radians) by which one oscillation leads or lags another.
B1 each
Q4Progressive waves (phase, intensity, CRO) · Standard · Paper 2 style · 4 marks
A microphone connected to a cathode-ray oscilloscope (CRO) detects a sound wave. The time-base is set at 2.0 ms per division and the Y-gain at 0.50 V per division. One complete cycle of the trace occupies 4.0 horizontal divisions and the vertical distance from a crest to a trough is 5.2 divisions.
(a)Determine the frequency of the sound.[2]
(b)Determine the amplitude of the signal.[1]
(c)The speed of sound in air is 340 m s⁻¹. Calculate the wavelength of the sound.[1]
Show answer
(a) 125 Hz
T = 4.0 × 2.0 ms = 8.0 ms (C1); f = 1/0.0080 = 125 Hz (A1)
Q6Progressive waves (phase, intensity, CRO) · Standard · Paper 2 style · 5 marks
A transverse wave of frequency 15 Hz travels along a long rope at a speed of 6.0 m s⁻¹.
(a)Calculate the wavelength of the wave.[1]
(b)Point X on the rope is 0.10 m from point Y and point Z is 0.20 m from Y, all along the direction of travel. Calculate the phase difference, in radians, between(i) X and Y, (ii) Z and Y.[2]
(c)At one instant Y is at a crest. Describe the displacement and motion of Z at that instant.[2]
(c) Z is at a trough (maximum negative displacement) and momentarily at rest.
B1 trough/maximum displacement in opposite direction; B1 instantaneously at rest
Q7Progressive waves (phase, intensity, CRO) · Standard · Paper 1 style · 1 mark
(a)The amplitude of a sound wave increases by 50 %. By what factor does its intensity increase?[1]
Show answer
(a) B 2.25
I ∝ A², so the factor is 1.5² = 2.25. 1.5 assumes intensity is proportional to amplitude.
Q8Progressive waves (phase, intensity, CRO) · Challenge · Paper 2 style · 5 marks
A small loudspeaker at an open-air event emits sound of power 0.60 W uniformly in all directions. Assume no energy is absorbed by the air.
(a)Define intensity.[1]
(b)Calculate the intensity of the sound at a distance of 5.0 m from the loudspeaker.[2]
(c)Determine the distance from the loudspeaker at which the amplitude of the sound wave is half its value at 5.0 m.[2]
Show answer
(a) Power transmitted per unit area (perpendicular to the direction of travel).
B1
(b) 1.9 × 10⁻³ W m⁻²
I = P/(4πr²) = 0.60/(4π × 5.0²) (C1) = 1.9 × 10⁻³ W m⁻² (A1)
(c) 10 m
amplitude halved → intensity ÷ 4 (C1); I ∝ 1/r² so r doubles to 10 m (A1)
Q9Progressive waves (phase, intensity, CRO) · Challenge · Paper 2 style · 6 marks
Two microphones A and B lie on a straight line from a loudspeaker, with B further from the speaker than A. Their signals are shown on a two-trace CRO with time-base 0.50 ms per division. One cycle of each trace occupies 6.0 divisions and the trace from B is shifted 1.5 divisions to the right (lagging) relative to that from A.
(a)Calculate the frequency of the sound.[2]
(b)Determine the phase difference between the two signals.[1]
(c)Microphone B is moved slowly further from the source along the line from the source. Calculate the extra distance it must be moved, from its original position, before the two traces are next in phase. The speed of sound is 340 m s⁻¹.[3]
Show answer
(a) 333 Hz
T = 6.0 × 0.50 ms = 3.0 ms (C1); f = 1/0.0030 = 333 Hz (A1)
(b) 90° (π/2 rad)
1.5/6.0 × 360° = 90° (B1)
(c) 0.77 m
λ = 340/333 = 1.02 m (C1); B lags by ¼ cycle, so it must move a further ¾λ to lag by a whole cycle (C1); 0.75 × 1.02 = 0.765 ≈ 0.77 m (A1)
Q10Progressive waves (phase, intensity, CRO) · Challenge · Paper 2 style · 5 marks
A hospital ultrasound probe emits waves of frequency 2.5 MHz in short pulses. The speed of ultrasound in soft tissue is 1540 m s⁻¹.
(a)Calculate the wavelength of the ultrasound in the tissue.[2]
(b)Calculate the time between emission of a pulse and detection of its echo from a boundary 6.0 cm below the probe.[2]
(c)Each pulse contains 4 complete cycles. Calculate the length of one pulse in the tissue.[1]
Show answer
(a) 0.62 mm
λ = 1540/(2.5 × 10⁶) (C1) = 6.2 × 10⁻⁴ m (A1)
(b) 78 µs
distance = 2 × 0.060 = 0.12 m (C1); t = 0.12/1540 = 7.8 × 10⁻⁵ s (A1)
(c) 2.5 mm
4λ = 4 × 0.616 = 2.5 mm (B1)
Q11Polarisation (Malus) · Core · Paper 1 style · 1 mark
(a)Which type of wave cannot be polarised?[1]
Show answer
(a) C sound in air
Only transverse waves can be polarised. Sound in air is longitudinal; the other three are electromagnetic (transverse) waves.
Q12Polarisation (Malus) · Core · Paper 2 style · 3 marks
Unpolarised light of intensity 64 W m⁻² is incident on two polarising filters, one after the other.
(a)Calculate the intensity of the light after it has passed through the first polariser.[1]
(b)The transmission axis of the second polariser is at 30° to that of the first. Calculate the intensity of the light leaving the second polariser.[2]
Show answer
(a) 32 W m⁻²
Unpolarised light: half transmitted, 64/2 = 32 W m⁻² (B1)
(b) 24 W m⁻²
I = I₀ cos²θ = 32 cos² 30° (C1) = 24 W m⁻² (A1)
Q13Polarisation (Malus) · Standard · Paper 2 style · 3 marks
A beam of plane-polarised laser light passes through a polarising filter that can be rotated.
(a)State Malus's law.[1]
(b)Calculate the smallest angle through which the filter must be rotated from the position of maximum transmission so that the transmitted intensity is 20 % of the maximum.[2]
Show answer
(a) The transmitted intensity I = I₀ cos²θ, where θ is the angle between the plane of polarisation of the light and the transmission axis of the filter.
B1
(b) 63°
cos²θ = 0.20 (C1); θ = 63.4° (A1)
Q14Polarisation (Malus) · Standard · Paper 2 style · 4 marks
A microwave transmitter emits plane-polarised microwaves towards a receiver connected to a meter. With the receiver aligned with the transmitter, the reading is 0.80 mA.
(a)Assume the meter reading is proportional to the intensity received. Calculate the reading when the receiver is rotated through 60° about the beam axis.[2]
(b)Explain why the reading is zero when the receiver has been rotated through 90°.[2]
Show answer
(a) 0.20 mA
I = 0.80 cos² 60° (C1) = 0.20 mA (A1)
(b) The microwaves are plane-polarised; at 90° the receiver's axis is perpendicular to the plane of oscillation, so no component of the electric field oscillation is detected.
B1 transmitter emits plane-polarised waves; B1 cos 90° = 0 / no component along receiver axis
Q15Polarisation (Malus) · Challenge · Paper 2 style · 6 marks
Unpolarised light of intensity 40 W m⁻² passes through polariser 1 and then polariser 3, whose transmission axis is at 90° to that of polariser 1.
(a)Show that no light emerges from the arrangement when only polarisers 1 and 3 are present.[1]
(b)Polariser 2 is now placed between them with its axis at 45° to both. Calculate the intensity of the light that emerges from polariser 3.[3]
(c)Explain why inserting a filter, which absorbs light, increases the amount of light emerging.[2]
Show answer
(a) Their axes are at 90°, so I = I₁ cos² 90° = 0.
B1
(b) 5.0 W m⁻²
after 1: 40/2 = 20 W m⁻² (C1); after 2: 20 cos² 45° = 10 W m⁻² (C1); after 3: 10 cos² 45° = 5.0 W m⁻² (A1)
(c) Polariser 2 transmits a component of the light polarised at 45°; this light now has a component along the axis of polariser 3.
B1 light leaving 2 polarised at 45°; B1 has non-zero component along axis of 3
Q16Polarisation (Malus) · Challenge · Paper 2 style · 4 marks
Plane-polarised light of intensity 12.0 W m⁻² falls on a polarising filter. The angle between the plane of polarisation and the transmission axis of the filter is θ.
(a)Explain what is meant by plane-polarised light.[1]
(b)Calculate the transmitted intensity when θ is (i) 20° and (ii) 70°.[2]
(c)Explain why polarisation provides evidence that light is a transverse wave.[1]
Show answer
(a) Light in which the oscillations (of the electric field) occur in one plane only, which contains the direction of travel.
(c) Only transverse waves have oscillations perpendicular to the direction of travel that can be restricted to one plane.
B1
Q17Doppler effect · Core · Paper 2 style · 4 marks
An ambulance travels at 25 m s⁻¹ along a straight road in Rawalpindi. Its siren emits sound of frequency 950 Hz. A man stands at the roadside. The speed of sound in air is 340 m s⁻¹.
(a)Calculate the frequency heard by the man as the ambulance approaches.[2]
(b)Calculate the frequency he hears after it has passed.[2]
Q18Doppler effect · Core · Paper 2 style · 4 marks
(a)Explain, in terms of wavefronts, why a stationary observer hears a higher frequency when a sound source moves towards him.[2]
(b)A police car with a 700 Hz siren approaches at 30 m s⁻¹. The speed of sound is 330 m s⁻¹. Calculate the frequency heard.[2]
Show answer
(a) The source moves towards the observer between emitting successive wavefronts, so the wavefronts in front are closer together; the wavelength is shorter and, with the same wave speed, more wavefronts arrive per second.
B1 wavefronts bunched/shorter wavelength; B1 same speed so higher frequency received
(b) 770 Hz
f = 700 × 330/(330 − 30) (C1) = 770 Hz (A1)
Q19Doppler effect · Standard · Paper 1 style · 1 mark
(a)[1]
Show answer
(a) B 14.2 m s⁻¹
480 = 500 × 340/(340 + v_s) → 340 + v_s = 354.2 → v_s = 14.2 m s⁻¹. 13.6 m s⁻¹ uses 340 × (20/500), the formula for a moving observer.
Q20Doppler effect · Standard · Paper 2 style · 5 marks
A girl on a station platform hears the horn of a train passing at constant speed without stopping. The frequency she hears is 560 Hz as the train approaches and 480 Hz as it moves away. The speed of sound is 340 m s⁻¹.
(a)Show that the speed of the train is about 26 m s⁻¹.[3]
(b)Calculate the frequency emitted by the horn.[2]
Show answer
(a) 26.2 m s⁻¹
560 = f v/(v − u) and 480 = f v/(v + u) (C1); 560/480 = (v + u)/(v − u) (C1); 13u = v → u = 340/13 = 26.2 m s⁻¹ (A1)
(b) 517 Hz
f = 560 × (340 − 26.2)/340 (C1) = 517 Hz (A1)
Q21Doppler effect · Challenge · Paper 2 style · 5 marks
A small loudspeaker emitting a 1200 Hz note is attached to the end of a rod and moves in a horizontal circle of radius 0.80 m at 2.5 revolutions per second. A student stands far away in the plane of the circle. The speed of sound is 340 m s⁻¹.
(a)Calculate the speed of the loudspeaker.[1]
(b)Calculate the maximum and minimum frequencies heard by the student.[3]
(c)State the position of the loudspeaker when the student hears the frequency 1200 Hz. Explain your answer.[1]
(c) When it is moving perpendicular to the line to the student (nearest and furthest points of the circle), there is no velocity component towards or away from her.
B1
Q22Electromagnetic spectrum · Core · Paper 1 style · 1 mark
(a)Which list places the regions of the electromagnetic spectrum in order of increasing wavelength?[1]
Show answer
(a) A γ-rays, X-rays, ultraviolet, visible, infrared, microwaves, radio waves
γ-rays have the shortest wavelength and radio waves the longest. B is the same list in order of decreasing wavelength.
Q23Electromagnetic spectrum · Core · Paper 2 style · 5 marks
(a)State the approximate range of wavelengths of visible light in a vacuum.[1]
(b)Calculate the frequency of orange light of wavelength 600 nm in a vacuum.[2]
(c)Name the region of the spectrum for a wavelength of (i) 3 cm, (ii) 1 × 10⁻¹⁰ m.[2]
Q24Electromagnetic spectrum · Standard · Paper 2 style · 4 marks
(a)State two properties shared by all electromagnetic waves in a vacuum.[2]
(b)Calculate the time for a radio signal to travel from the Earth to the Moon, a distance of 3.84 × 10⁸ m.[2]
Show answer
(a) Any two: same speed 3.00 × 10⁸ m s⁻¹; transverse; can be polarised; travel through a vacuum; consist of oscillating electric and magnetic fields.
B1 each, any two
(b) 1.28 s
t = 3.84 × 10⁸/3.00 × 10⁸ (C1) = 1.28 s (A1)
Q25Electromagnetic spectrum · Standard · Paper 1 style · 1 mark
(a)An electromagnetic wave has a frequency of 1.0 × 10¹⁰ Hz. In which region of the spectrum is it?[1]
Show answer
(a) B microwaves
λ = 3.0 × 10⁸/1.0 × 10¹⁰ = 0.030 m = 3 cm, which is in the microwave region. Radio waves have wavelengths longer than about 0.1–1 m.
Q26Electromagnetic spectrum · Challenge · Paper 2 style · 4 marks
A home router in Karachi transmits Wi-Fi signals at 2.4 GHz, and a local FM radio station broadcasts at 101 MHz.
(a)Calculate the wavelength of (i) the Wi-Fi signal, (ii) the FM radio signal.[2]
(b)A navigation satellite is 2.02 × 10⁷ m above a receiver. Calculate the time for its signal to reach the receiver.[1]
(c)A timing error of 1.0 µs is made in measuring this travel time. Calculate the resulting error in the calculated distance.[1]
Show answer
(a) (i) 0.125 m (ii) 2.97 m
(i) 3.00 × 10⁸/2.4 × 10⁹ = 0.125 m (B1); (ii) 3.00 × 10⁸/101 × 10⁶ = 2.97 m (B1)
(b) 0.0673 s
2.02 × 10⁷/3.00 × 10⁸ = 0.0673 s (B1)
(c) 300 m
3.00 × 10⁸ × 1.0 × 10⁻⁶ = 300 m (B1)
Q27Transverse & longitudinal waves · Core · Paper 2 style · 4 marks
(a)Distinguish between a transverse wave and a longitudinal wave.[2]
(b)Give one example of each type of wave.[2]
Show answer
(a) Transverse: oscillations perpendicular to the direction of energy transfer. Longitudinal: oscillations parallel to the direction of energy transfer.
B1 each
(b) Transverse: light / any EM wave / waves on a string. Longitudinal: sound / ultrasound / P-waves.
B1 each
Q28Transverse & longitudinal waves · Core · Paper 1 style · 1 mark
(a)In which wave do the particles of the medium oscillate parallel to the direction in which the wave transfers energy?[1]
Show answer
(a) C sound in air
Sound in air is longitudinal. A guitar-string wave is transverse: the string moves perpendicular to the wave direction.
Q29Transverse & longitudinal waves · Standard · Paper 2 style · 5 marks
One end of a long stretched slinky spring is pushed and pulled along its length at 2.5 Hz. The distance between the centres of two adjacent compressions is 0.72 m.
(a)Explain what is meant by a compression and a rarefaction.[2]
(b)Calculate the speed of the wave.[2]
(c)State the distance between a compression and the nearest rarefaction.[1]
Show answer
(a) Compression: region where the coils (particles) are closer together than normal; rarefaction: region where they are further apart than normal.
B1 each
(b) 1.8 m s⁻¹
λ = 0.72 m (C1); v = 2.5 × 0.72 = 1.8 m s⁻¹ (A1)
(c) 0.36 m
λ/2 (B1)
Q30Transverse & longitudinal waves · Challenge · Paper 2 style · 4 marks
An earthquake produces longitudinal P-waves travelling at 6.0 km s⁻¹ and transverse S-waves travelling at 3.5 km s⁻¹ through rock. A seismic station in Quetta records the S-waves arriving 24 s after the P-waves.
(a)Calculate the distance from the earthquake to the station.[3]
(b)S-waves do not pass through the Earth's liquid outer core. Suggest why.[1]
