Question

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

Answer 1

1. The relation between frequency, length of the string, and tension in the string is given by $f=\frac{1}{2L}\sqrt{\frac{T}{M}}$where, $f$ is the frequency of transverse vibrations in the stretched string, $L$is the length of the string, $T$ is the tension in the string and $M$ is the mass of the string.
2. The two ways by which the frequency of transverse vibrations of a stretched string can be decreased are:

i. By increasing the length $\left(L\right)$, when tension $\left(T\right)$ and mass $\left(m\right)$are kept constant.

ii. By decreasing the tension $\left(T\right)$, when length $\left(L\right)$ and mass $\left(m\right)$ are kept constant.

Hence two ways are by increasing the length $\left(L\right)$ of the string and decreasing the tension$\left(T\right)$ of the string.