Question

How is the frequency of a stretched string related to its length?

Answer 1

Transverse waves are produced in the stretched string. Frequency of these waves depends on the tension in the stretched string as well as the its length.

More is the length of the string lesser is the frequency of transverse waves.

Frequency of transverse waves in a stretched string is given by -

Frequency $\nu =\frac{n}{2L}\sqrt{\frac{T}{\mu }}$

where $L$ is the length of wire, $T$ is the tension in wire and $\mu$ is the mass per unit length of wire.

Thus larger is the length of wire, lesser is the frequency.