Question

What is the wavelength for a third harmonic standing wave on a string with fixed ends if the two ends are 2.4 m apart?

Answer 1

`"1.6 m"`

Explanation:

Higher harmonics are formed by adding successively more nodes. The third harmonic has two more nodes than the fundamental, the nodes are arranged symmetrically along the length of the string.

One third the length of the string is between each node. The standing wave pattern is shown above in the image. From looking at the picture, you should be able to see that the wavelength of the third harmonic is two-thirds the length of the string.

`lambda_3 = (2/3)L = (2/3) × "2.4 m" = color(blue)"1.6 m"`

The frequency of third harmonic will be

`rArr f_3 = V/lambda_3 = (3V)/(2L)= 3f_1`