A Level Physics 7.1 Progressive Waves MCQs – 30 Practice Questions with Answers (Cambridge 9702)

Free practice MCQs for Cambridge International AS & A Level Physics (9702), Section 7.1 Progressive Waves. Work through wave basics and phase difference, wave graphs and intensity, then open each answer to check the full working.

Formula recap: wave speed v = fλ, period T = 1 / f, phase difference (in degrees) = (separation / λ) × 360°, intensity I = P / A, and for a progressive wave intensity is proportional to (amplitude)2. Keep the full A Level Physics Formula Sheet open while you practise.

Wave Basics & Phase Difference

Q1. What does a progressive (travelling) wave transfer from one place to another?

  • (A) Matter only
  • (B) Energy, without any overall transfer of matter
  • (C) Matter and energy together
  • (D) Neither matter nor energy
Show Answer

Answer: B – In a progressive wave the oscillations travel through the medium and carry energy with them, but the particles of the medium only vibrate about fixed positions; there is no overall flow of matter.

Q2. The frequency of a wave is best defined as

  • (A) the number of wavelengths that pass a point each second multiplied by the speed
  • (B) the time taken for one complete oscillation of a particle
  • (C) the number of complete oscillations of a particle per unit time
  • (D) the distance travelled by a wavefront in one second
Show Answer

Answer: C – Frequency f is the number of complete oscillations per unit time, measured in hertz (Hz). Option B defines the period T, and D describes the wave speed.

Q3. A progressive wave has frequency 5.0 Hz and wavelength 0.40 m. What is the speed of the wave?

  • (A) 0.080 m/s
  • (B) 12.5 m/s
  • (C) 45 m/s
  • (D) 2.0 m/s
Show Answer

Answer: D – v = fλ = 5.0 × 0.40 = 2.0 m/s.

Q4. A sound wave in air has frequency 250 Hz. What is its period?

  • (A) 4.0 × 10−3 s
  • (B) 0.25 s
  • (C) 4.0 s
  • (D) 250 s
Show Answer

Answer: A – T = 1 / f = 1 / 250 = 4.0 × 10−3 s.

Q5. Two points on a progressive wave are separated by exactly two complete wavelengths along the direction of travel. The phase difference between the oscillations at the two points is

  • (A) 0° (the points are in phase)
  • (B) 90°
  • (C) 180°
  • (D) 360°, so the points are in antiphase
Show Answer

Answer: A – A separation of a whole number of wavelengths is a whole number of cycles (here 720°), which is equivalent to 0°: the points oscillate in phase. Antiphase means a phase difference of an odd number of half cycles, e.g. 180°.

Q6. Points P and Q on a wave are separated by a distance of half a wavelength. What is the phase difference between P and Q?

  • (A) 45°
  • (B) 90°
  • (C) 180°
  • (D) 360°
Show Answer

Answer: C – Phase difference = (separation / λ) × 360° = 0.5 × 360° = 180°. The points are in antiphase: when P is at a crest, Q is at a trough.

Q7. On a progressive transverse wave, two adjacent particles are separated by three-quarters of a wavelength. Their phase difference is

  • (A) 90°
  • (B) 135°
  • (C) 270°
  • (D) 540°
Show Answer

Answer: C – Phase difference = (3/4) × 360° = 270°, which is 3π/2 rad. (540° would be one and a half cycles.)

Q8. A wave has wavelength 0.60 m. Two points along the wave are 0.45 m apart. What is the phase difference between them?

  • (A) 75°
  • (B) 135°
  • (C) 240°
  • (D) 270°
Show Answer

Answer: D – Separation as a fraction of a cycle = 0.45 / 0.60 = 0.75. Phase difference = 0.75 × 360° = 270°.

Q9. Which statement about the amplitude of a progressive wave is correct?

  • (A) It is the distance between two adjacent crests.
  • (B) It is the maximum displacement of a particle from its equilibrium position.
  • (C) It is the distance the wave travels in one period.
  • (D) It is the number of oscillations completed each second.
Show Answer

Answer: B – Amplitude is the maximum displacement from the equilibrium (undisturbed) position. A is the wavelength, C is also one wavelength, and D is the frequency.

Q10. A water wave travels at 1.5 m/s and the distance between adjacent crests is 0.30 m. What is the frequency of the wave?

  • (A) 0.20 Hz
  • (B) 0.45 Hz
  • (C) 2.0 Hz
  • (D) 5.0 Hz
Show Answer

Answer: D – The distance between adjacent crests is λ = 0.30 m. f = v / λ = 1.5 / 0.30 = 5.0 Hz.

Wave Graphs

Q11. A displacement-distance graph for a wave shows 3 complete wavelengths occupying a distance of 0.90 m, with a maximum displacement of 2.0 cm. What are the wavelength and the amplitude?

  • (A) λ = 0.30 m, amplitude = 2.0 cm
  • (B) λ = 0.90 m, amplitude = 2.0 cm
  • (C) λ = 0.30 m, amplitude = 4.0 cm
  • (D) λ = 2.7 m, amplitude = 1.0 cm
Show Answer

Answer: A – λ = 0.90 / 3 = 0.30 m. The amplitude is the peak displacement from the zero line, 2.0 cm (not the full crest-to-trough height of 4.0 cm).

Q12. The displacement-time graph for one particle of a medium carrying a progressive wave shows a period of 0.020 s. What is the frequency of the wave?

  • (A) 0.020 Hz
  • (B) 20 Hz
  • (C) 50 Hz
  • (D) 500 Hz
Show Answer

Answer: C – f = 1 / T = 1 / 0.020 = 50 Hz.

Q13. For the same wave, the displacement-distance graph gives λ = 0.25 m and the displacement-time graph gives T = 0.050 s. What is the wave speed?

  • (A) 0.0125 m/s
  • (B) 0.20 m/s
  • (C) 12.5 m/s
  • (D) 5.0 m/s
Show Answer

Answer: D – f = 1 / T = 1 / 0.050 = 20 Hz. Then v = fλ = 20 × 0.25 = 5.0 m/s.

Q14. A particle on a progressive transverse wave is at the peak of a crest at a particular instant. At that instant, the particle

  • (A) has its maximum speed
  • (B) is momentarily at rest
  • (C) is moving in the direction of travel of the wave
  • (D) has zero displacement
Show Answer

Answer: B – The particles oscillate in simple harmonic motion. At maximum displacement (a crest or a trough) the particle is momentarily stationary before moving back towards equilibrium; the speed is greatest as it passes through the equilibrium position.

Q15. On a displacement-time graph for a single particle, 5 complete oscillations take 0.10 s and the peak displacement is 3.0 mm. What are the frequency and amplitude?

  • (A) f = 0.50 Hz, amplitude = 3.0 mm
  • (B) f = 5.0 Hz, amplitude = 6.0 mm
  • (C) f = 50 Hz, amplitude = 3.0 mm
  • (D) f = 50 Hz, amplitude = 1.5 mm
Show Answer

Answer: C – T = 0.10 / 5 = 0.020 s, so f = 1 / 0.020 = 50 Hz. Amplitude is the maximum displacement, 3.0 mm.

Q16. A wavefront is best described as

  • (A) a line joining points that all oscillate in phase with each other
  • (B) a line showing the direction in which the wave energy travels
  • (C) the path followed by one particle of the medium
  • (D) a line joining the crests of neighbouring waves only at one instant
Show Answer

Answer: A – A wavefront is a line (or surface) joining adjacent points that are all in phase, such as a line through neighbouring crests. The line showing the direction of energy transfer is a ray, drawn perpendicular to the wavefronts.

Q17. A progressive transverse wave travels from left to right. At the instant shown on a displacement-distance snapshot, point X is on the slope just before a crest (on the side nearer the source) and is moving towards the crest position. Which statement about X is correct?

  • (A) X moves in the direction of travel of the wave.
  • (B) X moves at right angles to the direction of travel of the wave.
  • (C) X does not move at all; only the wave profile moves.
  • (D) X moves opposite to the direction of travel of the wave.
Show Answer

Answer: B – In a transverse wave each particle oscillates perpendicular to the direction of energy transfer (the direction of travel). Particles never travel along with the wave; they only oscillate up and down about their equilibrium positions.

Q18. A displacement-distance graph of a wave with λ = 0.80 m shows points M and N separated by 0.20 m along the wave. The phase difference between M and N is

  • (A) 25°
  • (B) 90°
  • (C) 144°
  • (D) 180°
Show Answer

Answer: B – 0.20 / 0.80 = 0.25 of a cycle, so the phase difference = 0.25 × 360° = 90° (π/2 rad).

Q19. Which quantity cannot be obtained from a displacement-time graph of one particle alone?

  • (A) The period of the wave
  • (B) The frequency of the wave
  • (C) The amplitude of the wave
  • (D) The wavelength of the wave
Show Answer

Answer: D – A displacement-time graph for one particle gives T, hence f = 1/T, and the amplitude. The wavelength is a distance, so it must come from a displacement-distance graph (or from λ = v/f if the speed is known).

Q20. A wave of frequency 3.0 Hz has a displacement-distance graph showing a wavelength of 2.0 m. What is the wave speed, and how far does a wavefront travel in 0.50 s?

  • (A) 6.0 m/s; 3.0 m
  • (B) 6.0 m/s; 12 m
  • (C) 1.5 m/s; 0.75 m
  • (D) 0.67 m/s; 0.33 m
Show Answer

Answer: A – v = fλ = 3.0 × 2.0 = 6.0 m/s. Distance = v × t = 6.0 × 0.50 = 3.0 m.


Intensity

Q21. The intensity of a progressive wave is defined as

  • (A) the power carried by the wave multiplied by the area it crosses
  • (B) the power per unit area crossing a surface at right angles to the direction of travel
  • (C) the energy carried by the wave per unit time
  • (D) the amplitude of the wave per unit area
Show Answer

Answer: B – Intensity I = P / A, measured in W/m2, where A is the area perpendicular to the direction of energy transfer.

Q22. A small source emits sound waves uniformly in all directions with a total power of 20 W. What is the intensity at a distance of 2.0 m from the source?

  • (A) 0.40 W/m2
  • (B) 1.6 W/m2
  • (C) 5.0 W/m2
  • (D) 10 W/m2
Show Answer

Answer: A – The power spreads over a sphere of area A = 4πr2 = 4π × (2.0)2 = 50.3 m2. I = P / A = 20 / 50.3 = 0.40 W/m2.

Q23. The amplitude of a progressive wave is doubled while its frequency is unchanged. The intensity of the wave becomes

  • (A) twice as large
  • (B) unchanged
  • (C) half as large
  • (D) four times as large
Show Answer

Answer: D – Intensity is proportional to (amplitude)2. Doubling the amplitude multiplies the intensity by 22 = 4.

Q24. A point source of waves has intensity 8.0 W/m2 at a distance of 1.0 m. Assuming the power spreads uniformly in all directions, the intensity at 2.0 m is

  • (A) 4.0 W/m2
  • (B) 2.0 W/m2
  • (C) 1.0 W/m2
  • (D) 16 W/m2
Show Answer

Answer: B – For a point source, I is proportional to 1/r2. Doubling r reduces I by a factor of 4: 8.0 / 4 = 2.0 W/m2.

Q25. The amplitude of a wave is increased to three times its original value. By what factor does the intensity change?

  • (A) 3
  • (B) 6
  • (C) 9
  • (D) 27
Show Answer

Answer: C – I is proportional to (amplitude)2, so the factor is 32 = 9.

Q26. At what distance from a point source will the intensity have fallen to one-ninth of its value at a distance of 0.50 m?

  • (A) 1.5 m
  • (B) 4.5 m
  • (C) 0.17 m
  • (D) 3.0 m
Show Answer

Answer: A – I is proportional to 1/r2. Reducing I to 1/9 requires r2 to increase by a factor of 9, so r increases by a factor of 3: 0.50 × 3 = 1.5 m.

Q27. A wave of fixed amplitude has its frequency doubled. Given that intensity is proportional to (frequency)2 × (amplitude)2, the new intensity is

  • (A) twice the original
  • (B) the same as the original
  • (C) eight times the original
  • (D) four times the original
Show Answer

Answer: D – With the amplitude fixed, doubling f multiplies I by 22 = 4.

Q28. A beam of power 3.0 W passes through a circular opening of radius 0.10 m, spread evenly over the opening. What is the intensity of the beam at the opening?

  • (A) 30 W/m2
  • (B) 95 W/m2
  • (C) 300 W/m2
  • (D) 950 W/m2
Show Answer

Answer: B – A = πr2 = π × (0.10)2 = 0.0314 m2. I = P / A = 3.0 / 0.0314 = 95 W/m2.

Q29. The amplitude of a sound wave is reduced to half of its original value, and the listener also moves to twice the original distance from the (point) source. The intensity at the listener, from the amplitude change alone combined with the distance change, becomes

  • (A) 1/4 of the original
  • (B) 1/8 of the original
  • (C) 1/16 of the original
  • (D) 1/2 of the original
Show Answer

Answer: C – Halving the amplitude gives a factor of (1/2)2 = 1/4. Doubling the distance from a point source gives 1/22 = 1/4. Combined: 1/4 × 1/4 = 1/16 of the original intensity.

Q30. Which change, on its own, would NOT alter the intensity of a progressive wave measured at a fixed point?

  • (A) Increasing the amplitude of the source
  • (B) Moving further from a point source
  • (C) Increasing the wavelength while keeping frequency and amplitude unchanged
  • (D) Increasing the frequency at constant amplitude
Show Answer

Answer: C – Intensity depends on (amplitude)2 and (frequency)2, and on the area over which the power spreads. Changing λ alone, with f and amplitude fixed (so the speed changes), does not change I = P/A at that point. A, B and D all change the intensity.

Keep going: browse all boards on the Physics MCQs hub, and revise every equation with the A Level Physics Formula Sheet.

All questions are original practice questions written for QuaidianPoint – they are not Cambridge past-paper questions. QuaidianPoint is not affiliated with Cambridge Assessment International Education.