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

3.28 m

Step-by-step explanation

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

`L=(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=(5)/(2)\cdot\lambda`

Solving for the wavelength λ,

`\lambda=(2)/(5)\cdot8.2m=3.28m`

The wavelength of this wave is 3.28 m.