Transverse and longitudinal waves, wave properties and wave speed (RP8) – GCSE Physics exam questions with mark scheme

1Grade 1–33 marks

The graph shows a transverse wave at one instant.

(a) Determine the amplitude of the wave. [1]

(b) Determine the wavelength of the wave. [1]

(a) 3 cm (do not accept 6 cm, peak to trough)(1)
(b) 20 cm(1)
(c) any one from: light / any named electromagnetic wave / ripples or waves on the surface of water / waves on a string / seismic S-waves (do not accept sound or ultrasound)(1)
Answer: (a) 3 cm (b) 20 cm (c) e.g. light
Examiner tip: Amplitude is measured from the middle (rest position) to a peak, not from peak to trough.

2Grade 4–54 marks

(a) A radio wave has a frequency of $9.0 \times 10^{7}$ Hz. The speed of radio waves is $3.0 \times 10^{8}$ m/s.

Calculate the wavelength of the radio wave. [3]

(b) Calculate the period of a wave with a frequency of 50 Hz. [1]

(a) $3.0 \times 10^{8} = 9.0 \times 10^{7} \times \lambda$ (substitution into $v = f\lambda$)(1)
(a) $\lambda = \dfrac{3.0 \times 10^{8}}{9.0 \times 10^{7}}$ (correct rearrangement)(1)
(a) 3.3 m (allow 3.33 m or 3⅓ m; a correct answer with no working scores 3 marks)(1)
(b) 0.02 s ($T = 1 \div 50$; allow 0.020 s or 1/50 s)(1)
Answer: (a) 3.3 m (b) 0.02 s
Examiner tip: Check powers of ten when dividing standard form numbers: 10⁸ ÷ 10⁷ = 10¹.

3Grade 6–75 marks

A student uses a ripple tank to measure the speed of water waves.

She counts 12 waves passing a point in 4.0 s. Using a ruler held just above the water, she measures that 10 wavelengths cover a distance of 45 cm.

(a) Calculate the frequency of the waves. [1]

(b) Calculate the speed of the waves in m/s. [3]

(a) 12 ÷ 4.0 = 3.0 Hz (allow 3 Hz)(1)
(b) λ = 45 ÷ 10 = 4.5 cm = 0.045 m(1)
(b) v = 3.0 × 0.045 (allow ecf from (a))(1)
(b) 0.14 m/s (allow 0.135 m/s; a correct answer with no working scores 3 marks; 13.5 or 14 scores 2 marks — no conversion to m)(1)
(c) one wavelength is too small to measure accurately, so measuring across 10 and dividing reduces the (percentage) uncertainty / makes the measurement more accurate (allow 'the waves are moving so one wavelength is hard to measure')(1)
Answer: (a) 3.0 Hz (b) 0.14 m/s (c) reduces uncertainty
Examiner tip: Convert cm to m before using v = fλ when the answer is asked for in m/s.

4Grade 1–3Foundation4 marks

A student holds one end of a stretched slinky spring. She moves her hand backwards and forwards along the length of the spring. The diagram shows the wave produced at one instant.

(a) Name the parts of the wave labelled X and Y. [2]

(b) Describe the direction in which the coils of the spring vibrate compared with the direction of energy transfer. [1]

(a) X: compression (allow where the coils are close together)(1)
(a) Y: rarefaction (allow where the coils are spread out; do not accept 'expansion' alone)(1)
(b) (vibrations are) parallel to the direction of energy transfer (allow in the same direction as / along the direction of wave travel; ignore 'backwards and forwards' unless linked to the direction of travel)(1)
(c) transverse (wave)(1)
Answer: (a) X compression, Y rarefaction (b) parallel to the direction of energy transfer (c) transverse
Examiner tip: Students often swap compression and rarefaction; compression is where the coils (or particles) are squashed together.

5Grade 1–34 marks

A small cork floats on the surface of a still pond. A stone is dropped into the pond a few metres away and ripples spread out across the water. The ripples pass the cork.

(a) Ripples on water are transverse waves. State what is meant by a transverse wave. [1]

(b) Describe the motion of the cork as the ripples pass it. [1]

(c) Explain how the motion of the cork shows that it is the wave, and not the water, that travels across the pond. [2]

(a) the oscillations / vibrations are perpendicular to the direction of energy transfer (allow at right angles to the direction the wave travels)(1)
(b) (the cork) moves up and down (allow bobs / oscillates vertically; do not accept 'moves with the waves' or 'moves towards the edge')(1)
(c) the cork (and so the water) stays in the same place / does not move towards the edge of the pond (allow ends up where it started)(1)
(c) but the ripples / energy move outwards across the pond (allow the wave transfers energy, not water)(1)
Answer: (a) oscillations perpendicular to direction of energy transfer (b) up and down (c) cork stays in the same place while the ripples/energy travel outwards
Examiner tip: Saying the cork 'moves with the wave' loses the mark: it only moves up and down and is not carried along.

6Grade 6–75 marks

Two students measure the speed of sound in air on a school field. Student A stands 300 m away from student B. Student A bangs two wooden blocks together above his head. Student B starts a stopwatch when she sees the blocks hit and stops it when she hears the sound.

The table shows their results.

Trial	1	2	3	4
Time in s	0.92	0.85	1.21	0.88

(a) Identify the anomalous result. [1]

(b) Calculate the speed of sound in air. Ignore the anomalous result. [3]

(a) 1.21 (s) / trial 3(1)
(b) mean time = $\dfrac{0.92 + 0.85 + 0.88}{3}$ = 0.88 s (allow 0.883 s)(1)
(b) $v = \dfrac{300}{0.88}$ (allow speed = distance ÷ time with their mean time)(1)
(b) 340 m/s (allow 339–341 m/s; if anomalous result included, mean = 0.965 s, v = 311 m/s scores 2 marks max)(1)
(c) the time is longer, so the reaction time (of student B) is a smaller fraction of the measured time (allow reduces the (percentage) uncertainty / error due to reaction time; ignore 'more accurate' alone)(1)
Answer: (a) 1.21 s (b) 340 m/s (c) longer time means reaction time has less effect
Examiner tip: Leave the anomaly out of the mean, and in (c) link the bigger distance to reaction time being a smaller fraction of the time measured.

7Grade 6–7HigherTriple only5 marks

A sound wave travels through air and then into water. In air the sound wave has a speed of 330 m/s and a wavelength of 0.55 m.

(a) Calculate the frequency of the sound wave. [1]

(b) The speed of sound in water is 1500 m/s.

Calculate the wavelength of the sound wave in water. Give a reason for your method. [3]

(a) $f = \dfrac{330}{0.55}$ = 600 Hz(1)
(b) the frequency stays the same / is still 600 Hz (when the wave enters the water) (allow frequency depends only on the source)(1)
(b) $\lambda = \dfrac{1500}{600}$ (allow ecf from (a))(1)
(b) 2.5 m (allow ecf from (a))(1)
(c) the wavelength decreases (back to 0.55 m) (allow gets shorter; ignore references to frequency changing)(1)
Answer: (a) 600 Hz (b) 2.5 m, because the frequency does not change (c) wavelength decreases (back to 0.55 m)
Examiner tip: The frequency is fixed by the source; only speed and wavelength change when sound crosses into a new medium.

8Grade 6–76 marks

A student uses the equipment shown to investigate waves on a string.

When the signal generator is switched on, the vibration generator makes the string vibrate. At certain frequencies a clear wave pattern of loops can be seen, as in the diagram.

Describe how the student could use this equipment to determine the speed of the waves on the string. [6]

switch on the signal generator and adjust the frequency until a clear / stable (stationary) wave pattern is seen(1)
read the frequency from the signal generator (display)(1)
use a metre rule to measure the length of several whole loops (e.g. from the vibration generator to the pulley)(1)
count the number of loops; each loop is half a wavelength(1)
wavelength = 2 × (measured length ÷ number of loops)(1)
calculate wave speed using $v = f \lambda$(1)
measuring across several loops reduces the uncertainty in the wavelength(1)
repeat for different frequencies (or repeat each measurement) and calculate a mean value of speed(1)
keep the mass on the end of the string (tension) and the type of string the same, as these affect the wave speed(1)
allow use of a stroboscope or a photograph of the pattern next to a ruler to help measure the loops(1)

Level	Marks	What it looks like
Level 3	5–6	A coherent, logically ordered method that would allow the speed to be found: how a clear pattern is obtained, how frequency is read, how wavelength is found from the loops (including the half-wavelength link), and use of v = fλ, with at least one step to improve the reliability or accuracy.
Level 2	3–4	A method with the main measurements of frequency and wavelength and use of v = fλ, but with some steps missing or unclear (for example, the link between loops and wavelength not stated).
Level 1	1–2	Simple, disjointed statements about measuring something on the string or using the equipment, with little indication of how the speed is found.
No relevant content	0	Nothing worthy of credit.

Answer: Indicative method: adjust f until clear loops, read f from signal generator, measure length of n loops with a metre rule, λ = 2L/n, v = fλ, repeat at other frequencies and take a mean, keeping tension and string the same.
Examiner tip: Many answers forget that one loop is only half a wavelength; say how the wavelength is found from the loops before using v = fλ.

9Grade 8–9Higher6 marks

A student investigates how the depth of water in a ripple tank affects the speed of the water waves. The frequency of the waves is kept at 8.0 Hz. A lamp above the tank makes a pattern of shadows on a sheet of paper under the tank. The student measures the wavelength from the shadows.

Depth of water in cm	Wavelength in cm
0.5	2.8
1.0	3.9
1.5	4.8
2.0	5.5

(a) Calculate the speed of the waves, in m/s, when the depth of the water is 1.5 cm. [3]

(b) Describe the relationship between the depth of the water and the speed of the waves. Use the data. [1]

(c) The shadows on the paper are bigger than the waves on the water. Explain the effect this has on the student's values for wave speed. [2]

(a) 4.8 cm = 0.048 m (conversion seen)(1)
(a) $v = 8.0 \times 0.048$ (allow $v = f\lambda$ with their wavelength in m)(1)
(a) 0.38 m/s (allow 0.384 m/s; 38 cm/s or 38.4 scores 2 marks max)(1)
(b) as the depth increases the speed increases, but not in direct proportion (allow the speed increases by smaller amounts each time / doubling the depth does not double the speed)(1)
(c) the measured wavelengths are larger than the true wavelengths (allow the shadow wavelength is magnified)(1)
(c) so the calculated speeds are too high (allow speed overestimated; ignore 'inaccurate' alone; a systematic error, so the pattern is unaffected is not required)(1)
Answer: (a) 0.38 m/s (b) speed increases with depth but not proportionally (c) wavelengths too large so calculated speeds too large
Examiner tip: Convert cm to m before using v = fλ, and in (c) say which way the speed is wrong, not just that it is 'inaccurate'.

10Grade 4–54 marks

A microphone is connected to an oscilloscope. A loudspeaker produces a sound of constant frequency near the microphone. The graph shows the trace on the oscilloscope screen.

(a) Use the graph to determine the period of the sound wave. [1]

(b) Calculate the frequency of the sound wave. [1]

(a) 2.5 ms (allow 0.0025 s; allow 2.4–2.6 ms)(1)
(b) $f = \dfrac{1}{T} = \dfrac{1}{0.0025}$ = 400 Hz (allow 0.4 kHz; allow ecf from (a))(1)
(c) $\lambda = \dfrac{v}{f}$ or $340 = 400 \times \lambda$ (allow ecf for f from (b))(1)
(c) 0.85 m (allow ecf from (b) correctly calculated)(1)
Answer: (a) 2.5 ms (b) 400 Hz (c) 0.85 m
Examiner tip: Read the period over several cycles (4 cycles take 10 ms) and convert ms to s before using f = 1/T.

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