This is an activity from the AS unit *The Sound of Music* and is one of many looking at the physics of sound. It will probably be the first occasion that the students will have used the Spectrum Analyser so an introduction to its use would be wise.

The microphone on DrDAQis ideally suited to this task. Needless to say, other recorders being played at the same time will also get recorded. The playing of a number of them needs to be controlled.

Additional frequencies could be obtained by the playing of a tenor or bass recorder.

If students are already competent with drawing best-fit lines and calculating gradients then they might like to use a spreadsheet here instead, the data collected being placed into one and the appropriate graph and best-fit line plotted.

Answers to questions

1 Taking the speed of sound *v *to be constant, *f* will then be inversely
proportional to *l* and so the graphs will be as in Figure T11.1

Figure T11.1 Graphs of (a) *f* against *l* and (b) *f* against 1/*l*

2 Writing the equation as

*f = v*/2 * * *´* * *1/ *l *and comparing with *y = mx + c * the gradient must be
equal to *v*/2.

The results obtained should compare very favourably, but there will be inaccuracies in the measurements of the length of the standing waves and in the precise value of the fundamental frequency as indicated by the spectrum analyser.

The inability of the best-fit line to pass through the origin could best be explained by a consistent error in determining the length of the standing waves.

Results

Note |
Frequency /Hz | l /m | 1/l m ^{-1} |

C | 536 | 0.326 | 3.07 |

D | 607 | 0.279 | 3.58 |

E | 686 | 0.253 | 3.95 |

F | 747 | 0.234 | 4.27 |

G | 809 | 0.210 | 4.76 |

A | 926 | 0.187 | 5.35 |

B | 1024 | 0.168 | 5.95 |

Figure T11.2 Table of results

See attached.

Figure T11.3 Graph of Frequency against 1/Length of standing wave

PC running PicoScope

Descant and other recorders

Disinfecting solution

0.5 m/1 m rule

Between use do ensure that the mouthpieces of the recorders are disinfected.

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