| Date | November 2015 | Marks available | 1 | Reference code | 15N.3.SL.TZ0.2 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 0 |
| Command term | Show that | Question number | 2 | Adapted from | N/A |
Question
This question is about sound waves.
A whistle on a steam train consists of a pipe that is open at one end and closed at the other. The sounding length of the whistle is 0.27 m and the steam pressure in the whistle is so great that the third harmonic of the pipe is sounding. The speed of sound in air is \({\text{340 m}}\,{{\text{s}}^{ - 1}}\).
Show that there must be a node at a distance of 0.18 m from the closed end of the pipe.
Calculate the frequency of the whistle sound.
The train is moving directly away from a stationary observer at a speed of \({\text{22 m}}\,{{\text{s}}^{ - 1}}\) while the whistle is sounding. Calculate the frequency heard by the observer.
Markscheme
third harmonic means 1.5 loops; (accept in form of a diagram)
\(\frac{2}{3} \times 0.27{\text{ }}( = 0.18)\);
length is \(\frac{3}{4}\) of a wavelength so \(\lambda = 0.36{\text{ m}}\);
\(f = 940{\text{ (Hz)}}\);
\(f' = 940\left( {\frac{{340}}{{340 + 22}}} \right)\); (allow ECF from (a)(ii))
880 (Hz);
Examiners report
Many candidates drew the 5th harmonic, not realising that the harmonic number is related to the multiple of the frequency which is only odd in “closed” pipes. This was not penalised in ECF.
Many candidates drew the 5th harmonic, not realising that the harmonic number is related to the multiple of the frequency which is only odd in “closed” pipes. This was not penalised in ECF.
Many candidates drew the 5th harmonic, not realising that the harmonic number is related to the multiple of the frequency which is only odd in “closed” pipes. This was not penalised in ECF.
