Question 1

Paper 2Easy9 marks

A string on a musical instrument is fixed at both ends and vibrates in the mode shown in Figure 1.

00.10.20.30.40.50.6-2.5-2-1.5-1-0.500.511.522.5position, x / mdisplacement, y / mmAB
(a)

State the number of displacement nodes and the number of antinodes shown. Count the fixed ends as nodes.

[2]
(b)

The string has length 0.600 m0.600\ \mathrm{m} and the wave speed on it is 120 m s−1120\ \mathrm{m\,s^{-1}} For the mode shown, calculate the wavelength and frequency. Give both answers to 3 significant figures.

[3]
(c)

Compare the oscillation amplitudes at A and B, and state their phase difference.

[2]
(d)

Sound travels at 340 m s−1340\ \mathrm{m\,s^{-1}} in a pipe of length 0.600 m0.600\ \mathrm{m} The pipe is closed at one end and open at the other. Calculate the wavelength and frequency of the third harmonic. Ignore end correction.

[2]

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