Question

State two ways by which the frequency of transverse vibrations of a stretched string can be increased.

Answer 1

$\left(i\right)$ The frequency of transverse vibrations of a stretched string is inversely proportional to the length of the string i.e., frequency can be increased by decreasing the length of the string.
Frequency of string $\propto \frac{1}{\text{length of the string}}$

$f=\frac{1}{2L}\sqrt{\frac{T}{M}}$

where f = frequency of transverse vibrations in the streched string,

L = length of the string

T = tension in the string

M = mass of the string

$\left(ii\right)$ The frequency can be increased by increasing the tension in the string.

The frequency of transverse vibrations of a stretched string is directly proportional to the square root of the tension in the string.