This question is about the Doppler effect.

The diagram shows wavefronts in air produced by a stationary source S of sound. The distance between successive wavefronts is equal to the wavelength of the sound. The speed of sound is *c*.

a.On the diagram, sketch three successive wavefronts produced when S is moving to the left at a speed of 0.5*c*.[2]

(i) Determine the speed of a point on the edge of the turntable.

(ii) State the assumption you made in your answer to (b)(i).[3]

**▶️Answer/Explanation**

## Markscheme

a.

3 circular wavefronts;

2 centres/sources of wavefronts move left (by one box);

*Drawn circular wavefronts may be larger as in diagram here, or could be equal sized. Both are acceptable. *

(i) \(v = \frac{{5 \times {{10}^{ – 16}} \times 3 \times {{10}^8}}}{{7.5 \times {{10}^{ – 9}}}}\);

20(ms–1);*Use of sound equation not acceptable. *

(ii) assume speed of X-rays \( = \) *c */ assume speed of turntable << *c*;

This question is about the Doppler effect.

Georgia carries out an experiment to measure the speed of mosquitoes. She sets up a microphone to record the sounds of passing mosquitoes.

One mosquito is moving in a straight line with constant speed and passes very close to the microphone as seen in the diagram. The mosquito produces a sound of constant frequency.

a.The speed of sound in air is \({\text{340 m}}\,{{\text{s}}^{ – {\text{1}}}}\).

The maximum frequency recorded is 751 Hz and the minimum frequency recorded is 749 Hz. Explain this observation.[2]

**▶️Answer/Explanation**

## Markscheme

a.

as the mosquito approaches the wavelength perceived by Georgia is shorter and therefore the perceived frequency is higher;

as the mosquito is moving away, the wavelength perceived is longer than the emitted and therefore the perceived frequency is lower;

due to the Doppler effect;

approaching \(751 = f \times \frac{{340}}{{340 – u}}\);

moving away \(749 = f \times \frac{{340}}{{340 + u}}\);

to produce \(u = 0.45{\text{ m}}\,{{\text{s}}^{ – 1}}\);

*or*

emitted frequency is \(\frac{{751 + 749}}{2} = 750{\text{ Hz}}\);

applying the Doppler effect for approach (or recession), \(751 = 750\frac{{340}}{{340 – u}}\)\(\,\,\,\)** or**\(\,\,\,\)\(749 = 750\frac{{340}}{{340 + u}}\);

to produce \(u = 0.45{\text{ m}}\,{{\text{s}}^{ – 1}}\);