Question

A string length is 8.2 meters and is vibrating as the fifth harmonic. The string vibrates up and down with 12 cycles in 4 seconds. Determine the wavelength for this wave.

Answer 1

ANSWER

3.28 m

EXPLANATION

The length of the string and the wavelength when the string is vibrating as its nth harmonic is related by,

$L=\frac{n}{2}\cdot\lambda$

In this problem, we are given the length of the string L = 8.2 m and we have to find the wavelength for this wave when the string is vibrating as the 5th harmonic,

$8.2m=\frac{5}{2}\cdot\lambda$

Solving for the wavelength λ,

$\lambda=\frac{2}{5}\cdot8.2m=3.28m$

The wavelength of this wave is 3.28 m.