Question

A string that is fixed at both ends has a length of 2.79 m. When the string vibrates at a frequency of 85.7 Hz, a standing wave with five loops is formed. (a) What is the wavelength of the waves that travel on the string? (b) What is the speed of the waves? (c) What is the fundamental frequency of the string?

Answer 1

A standing wave with 5 loops tells you that 85.7 Hz is the frequency of the 5th harmonic of the string.

a) In general, if L is the length of the string,
the nth harmonic has wavelength given by= 2L/n.

Here L = 2.79 m and n = 5, so the wavelength is= 2*2.79/5 = 1.116 m

b) In general, for any wave

, v =speed = frequency times wavelength.

We know the frequency and the wavelength,

f = 85.7 Hz, wavelength= 1.116m,

so v = (85.7.3 Hz)(1.116m) = 95.6412m/s.

c) In general, the frequency of the nth harmonic is n times the frequency of the fundamental,

so that tells you the fundamental frequency is

85.7 Hz/5 = 17.14 Hz.

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