| Date | May 2014 | Marks available | 2 | Reference code | 14M.3.SL.TZ2.2 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 2 |
| Command term | Describe | Question number | 2 | Adapted from | N/A |
Question
This question is about the Doppler effect.
A child on a carousel (merry-go-round) moves with a speed of \({\text{6.5 m}}\,{{\text{s}}^{ - 1}}\) along a horizontal circular path ABCDA. A stationary observer is at a large distance from the carousel.
The child blows a whistle while moving from position B to position D. The whistle emits sound of frequency 850 Hz. The speed of sound in air is \({\text{330 m}}\,{{\text{s}}^{ - 1}}\).
Describe what is meant by the Doppler effect.
(i) Determine the minimum frequency of the sound heard by the observer.
(ii) Describe the variation of the frequency of the sound heard by the observer.
Markscheme
change in the observed/perceived frequency;
when there is relative motion between the source and the observer / when either the source or observer is moving;
(i) \(f = 850\left[ {\frac{{330}}{{330 + 6.5}}} \right]\);
\(f = 830{\text{ (Hz)}}\);
Award [1 max] for correct answer if moving observer equation is used with 6.5 in the numerator or if the approximate formula is used.
(ii) frequency increases;
(from 830 (Hz)) to 870 (Hz);
Examiners report
(a) was usually answered correctly, but it is worth emphasising that it is the perceived frequency that changes.
In (i) there were many correct answers, but sometimes the wrong Doppler equation was used or an incorrect sign convention chosen. Having found the minimum frequency (at position B) the vast majority then stated, in (ii), that frequency decreased from B to C. This is a question that needs careful discussion in class with future candidates.
