Question

The fundamental frequency of certain string under some tension is $n$ . If $25$ such similar strings but half length each are twisted together and stretched under same tension. Then the fundamental frequency of the system becomes

• A. $\frac{5n}{2}$
• B. $5n$
• C. $\frac{n}{5}$
• D. $\frac{2n}{5}$

Answer 1

The correct option is D $\frac{2n}{5}$

The equation for the fundamental frequency of an ideal taut string is:

$n=\frac{1}{2l}\sqrt{\frac{T}{\mu }}$ ,where $\mu$ is mass per unit length.

now when we have 25 string with length $l/2$

${\mu }_1=25\mu$ and tension remains the same

$n_1=\frac{1}{2l/2}\sqrt{\frac{T}{25\mu }}$

$n_1=\frac{2n}{5}$