| Date | May 2014 | Marks available | 4 | Reference code | 14M.3.SL.TZ1.2 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 1 |
| Command term | Calculate, Deduce, Describe, and Show that | Question number | 2 | Adapted from | N/A |
Question
This question is about standing waves and the Doppler effect.
The horn of a train can be modeled as a pipe with one open end and one closed end. The speed of sound in air is 330ms–1.
On leaving the station, the train blows its horn. Both the first harmonic and the next highest harmonic are produced by the horn. The difference in frequency between the harmonics emitted by the horn is measured as 820 Hz.
(i) Deduce that the length of the horn is about 0.20 m.
(ii) Show that the frequency of the first harmonic is about 410 Hz.
(i) Describe what is meant by the Doppler effect.
(ii) The train approaches a stationary observer at a constant velocity of 50ms–1 and sounds its horn at the same frequency as in (a)(ii). Calculate the frequency of the sound as measured by the observer.
Markscheme
(i) \({f_1} = \frac{v}{{4L}}\), \({f_2} = 3{f_1} = \frac{{3v}}{{4L}}\);
\({f_2} - {f_1} = \frac{v}{{2L}} = 820\left( {{\rm{Hz}}} \right)\);
\(L = \frac{{330}}{{2 \times 820}}\);
(L=0.20m)
(ii) \(\lambda = 4L = 0.80\left( {\rm{m}} \right)\);
\(f = \left( {\frac{{330}}{{0.8}}} \right) = 413 {\rm{Hz}}\);
This is a question testing units for this option. Do not award second marking point for an incorrect or missing unit.
(i) a change in the observed frequency/wavelength of a wave;
when there is relative motion of observer and source;
(ii) \(f'\left( { = f\frac{v}{{v - {u_s}}}} \right) = 410 \times \frac{{330}}{{330 - 50}}\);
\(f' = 480\left( {{\rm{Hz}}} \right)\);
Allow ECF from (a)(ii).
