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**.

**please like. thank you**

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