AQA A-Level Physics: Waves (7408) – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

These questions cover section 3.3 Waves of the AQA AS and A-level Physics specification (7407/7408, version 1.4, AS and A-level exams June 2016 onwards): 3.3.1 Progressive and stationary waves and 3.3.2 Refraction, diffraction and interference, including Required practicals 1 and 2. Waves is AS and A-level content, assessed at A-level in Paper 1 and assumed in Paper 2; it is not one of the Paper 3 Section B options (sections 3.9 to 3.13).

Learn the content first with the study guide. Take c = 3.00 × 10⁸ m s⁻¹ and the refractive index of air as 1.00.

Questions

1. State what is meant by a transverse wave and by a longitudinal wave. Give one example of each. [4]

2. A sound wave travelling at 330 m s⁻¹ has a period of 2.5 ms.

(a) Calculate its frequency. [1] (b) Calculate its wavelength. [2]

3. A wave of frequency 50 Hz travels along a rope at 12 m s⁻¹. Points P and Q on the rope are 0.18 m apart along the direction of travel. Calculate the phase difference between P and Q in radians. [3]

4.

(a) Explain why light can be polarised but sound cannot. [2] (b) Explain why the rods of a receiving aerial should be aligned in a particular direction. [2]

5.

(a) Explain, using the principle of superposition, how a stationary wave forms on a string fixed at both ends. [3] (b) State two differences between a stationary wave and a progressive wave. [2]

6. In Required practical 1, a string of length 0.65 m and mass per unit length 1.2 × 10⁻³ kg m⁻¹ vibrates in its first harmonic at 196 Hz.

(a) Calculate the tension in the string. [3] (b) State the frequency of the third harmonic and the number of nodes it has, including the ends. [2] (c) The string is replaced by one with four times the mass per unit length. Length and tension are unchanged. State the new first-harmonic frequency. [1] (d) Describe how to measure the mass per unit length of the string accurately. [2]

7. A microwave transmitter faces a metal plate. A probe moved along the line between them detects a series of minima.

(a) Explain why minima form. [2] (b) The probe moves 8.4 cm from the 1st minimum to the 7th minimum. Calculate the frequency of the microwaves. [3]

8. A laser lights a double slit and fringes form on a screen.

(a) State what is meant by coherent sources. [1] (b) 11 bright fringes span 15.0 mm on a screen 2.40 m from slits 0.90 mm apart. Calculate the wavelength. [3] (c) Describe the pattern seen if the laser is replaced by a white-light source and a single slit. [2] (d) State one safety precaution when using the laser. [1]

9.

(a) Derive the equation d sin θ = nλ for a diffraction grating at normal incidence. [3] (b) A grating with 400 lines per mm is lit normally with light of wavelength 546 nm. Calculate the angle of the second-order maximum. [2] (c) Determine the highest order that can be seen. [2]

10. Monochromatic light passes through a single narrow slit onto a screen.

(a) State the effect on the width of the central maximum of making the slit narrower. [1] (b) State the effect of replacing red light with blue light. [1] (c) Describe the pattern seen with white light. [2]

11. A step-index optical fibre has a core of refractive index 1.50 and cladding of refractive index 1.40.

(a) Calculate the speed of light in the core. [1] (b) Calculate the critical angle at the core–cladding boundary. [2] (c) Calculate the largest angle of incidence at the end of the fibre (in air) for which light is totally internally reflected at the core–cladding boundary. [3] (d) Explain how material and modal dispersion cause pulse broadening, and state how each can be reduced. [4]

12. Two loudspeakers connected to the same signal generator emit sound of frequency 680 Hz. The speed of sound is 340 m s⁻¹.

(a) Calculate the wavelength. [1] (b) Point X is 4.25 m from one loudspeaker and 5.00 m from the other. Determine whether X is a point of loud or quiet sound. [3] (c) Suggest why the sound at X is not completely silent. [1] (d) Explain why two loudspeakers on separate signal generators do not give a steady pattern. [2]

Answers

1. Transverse: oscillations are perpendicular to the direction of energy propagation [1]. Example: any EM wave or a wave on a string [1]. Longitudinal: oscillations are parallel to the direction of energy propagation [1]. Example: sound [1]. [4] Examiner insight: “Direction of the wave” is weaker than “direction of energy propagation”; an example only scores if it matches the correct definition.

2. (a) f = 1/T = 1/(2.5 × 10⁻³) = 400 Hz [1] (b) λ = c/f = 330/400 [1] = 0.83 m (0.825 m) [1] [3] Examiner insight: An error in (a) carried into (b) is normally allowed as error carried forward, so show the substitution.

3. λ = c/f = 12/50 = 0.24 m [1]. x/λ = 0.18/0.24 = 0.75 of a cycle [1]. Phase difference = 0.75 × 2π = 3π/2 rad (4.71 rad) [1] [3] Examiner insight: An answer of 270° does not earn the final mark when radians are asked for.

4. (a) Light is transverse, so its oscillations can be restricted to one plane [1]. Sound is longitudinal; its oscillations are along the direction of travel, so there is no other plane to filter out [1]. (b) The transmitted radio waves are plane polarised [1]. The aerial picks up the strongest signal when its rods are aligned with the plane of polarisation [1]. [4] Examiner insight: Each 2-mark part needs two separate points; “it gets a better signal” alone scores nothing.

5. (a) A wave travels along the string and reflects at the fixed end [1]. The incident and reflected waves have the same frequency and travel in opposite directions, and superpose [1]. Where they always cancel, nodes form; where they always reinforce, antinodes form [1]. (b) Any two: a stationary wave stores energy rather than transferring it [1]; its amplitude varies from zero at nodes to maximum at antinodes, while a progressive wave’s amplitude is the same everywhere; points between adjacent nodes are in phase, while phase varies continuously along a progressive wave [1]. [5] Examiner insight: “Same frequency” and “opposite directions” are both needed; missing either loses the mark.

6. (a) T = μ(2lf)² [1] = 1.2 × 10⁻³ × (2 × 0.65 × 196)² [1] = 78 N (77.9 N) [1] (b) f₃ = 3 × 196 = 588 Hz [1]; 4 nodes [1] (c) f ∝ 1/√μ, so f = 196/2 = 98 Hz [1] (d) Measure a long length of the string (several metres) with a metre rule [1], weigh it on a balance and divide mass by length [1]. [8] Examiner insight: In (d) the reason for using a long length (smaller percentage uncertainty) is what makes the method “accurate”.

7. (a) Microwaves reflected from the plate travel back and superpose with the incident waves of the same frequency [1]. At minima the two waves are always in antiphase and cancel, forming nodes [1]. (b) 1st to 7th minimum = 6 × λ/2 = 3λ = 8.4 cm, so λ = 2.8 cm [1]. f = c/λ = 3.00 × 10⁸ / 0.028 [1] = 1.1 × 10¹⁰ Hz [1] [5] Examiner insight: Using 7 spacings instead of 6 loses the first mark; the later marks can still be earned by error carried forward.

8. (a) Same frequency and a constant phase difference [1]. (b) 10 fringe spacings, so w = 1.50 mm [1]. λ = ws/D = (1.50 × 10⁻³ × 0.90 × 10⁻³)/2.40 [1] = 5.6 × 10⁻⁷ m (563 nm) [1] (c) A white central fringe [1]; the other fringes are coloured spectra, blue nearest the centre, fading after a few fringes [1]. (d) Never look into the beam or its reflections (or: remove reflective surfaces) [1]. [7] Examiner insight: Dividing 15.0 mm by 11 instead of 10 is the usual error; units must be converted to metres before substituting.

9. (a) Light from adjacent slits travelling at angle θ has path difference d sin θ [1]. For a maximum the path difference must be a whole number of wavelengths, nλ [1]. So d sin θ = nλ, where n is the order [1]. (b) d = 1/(400 × 10³) = 2.5 × 10⁻⁶ m [1]. sin θ = 2 × 546 × 10⁻⁹ / 2.5 × 10⁻⁶ = 0.437, θ = 25.9° [1] (c) d/λ = 2.5 × 10⁻⁶ / 546 × 10⁻⁹ = 4.58 [1]. Highest order = 4 [1] [7] Examiner insight: A diagram with the path difference marked can earn the first mark of (a); rounding 4.58 up to 5 loses the final mark.

10. (a) The central maximum becomes wider [1]. (b) The central maximum becomes narrower (shorter wavelength) [1]. (c) A white central maximum [1]; side maxima are spectra, with blue nearest the centre [1]. [4] Examiner insight: The answer must give a direction (wider or narrower), not just “changes”.

11. (a) c_s = c/n = 3.00 × 10⁸ / 1.50 = 2.00 × 10⁸ m s⁻¹ [1] (b) sin θc = n₂/n₁ = 1.40/1.50 = 0.933 [1]; θc = 69.0° [1] (c) Angle of refraction at the end face = 90° − 69.0° = 21.0° [1]. 1.00 × sin i = 1.50 × sin 21.0° = 0.539 [1]; i = 32.6° (allow 32.5°) [1] (d) Material dispersion: different wavelengths travel at different speeds in the core, so parts of a pulse arrive at different times [1]; reduce with a monochromatic source [1]. Modal dispersion: rays take different paths of different lengths, so the pulse spreads out and may overlap the next pulse [1]; reduce with a very narrow (single-mode) core [1]. [10] Examiner insight: In (c) the 90° − θc step is the method mark; using θc directly in Snell’s law at the end face scores zero for the method.

12. (a) λ = v/f = 340/680 = 0.50 m [1] (b) Path difference = 5.00 − 4.25 = 0.75 m [1]. 0.75/0.50 = 1.5 wavelengths [1]. An odd number of half wavelengths, so destructive interference: quiet [1] (c) The waves arrive with different amplitudes because X is at different distances from the speakers (or because of reflections) [1]. (d) The sources are not coherent: their phase difference is not constant [1], so the positions of loud and quiet points keep changing [1]. [7] Examiner insight: “Quiet” with no path-difference working scores nothing; the conclusion mark depends on the 1.5λ step.

Where marks are usually lost

• Counting fringes or nodes instead of the spacings between them.
• Leaving mm, nm or MHz unconverted before substituting.
• Giving a phase difference in degrees when radians are asked for, or with no unit.
• Rounding the highest grating order up.
• Missing “constant phase difference” from a definition of coherence.
• Forgetting the 90° − θc step when a ray enters the end of a fibre.
• Swapping material and modal dispersion, or giving one remedy for both.
• Describing stationary-wave formation without “same frequency” and “opposite directions”.

Next steps

• Recap with the Waves revision notes.
• Go back to the Waves study guide for worked examples.
• Uncertainties for the required practicals: measurements revision notes.
• See the AQA A-Level Physics hub and the printable checklist.
• Try all free 10-minute diagnostics.
• Book a free trial class.

Official syllabus

AQA AS and A-level Physics specification (7407/7408), version 1.4, July 2026, for AS and A-level exams June 2016 onwards, published by AQA. Section 3.3 Waves.