Question

A string is stretched so that its length is increased by $\frac{1}{\eta }$ of its original length. The ratio of fundamental frequency of transverse vibration to that of fundamental frequency of longitudinal vibration will be

• A. $\eta :1$
• B. $1:\eta$
• C. $\sqrt{\eta }:1$
• D. $1:\sqrt{\eta }$

Answer 1

The correct option is D $1:\sqrt{\eta }$

For transverse waves, speed will be proportional to length by the following relation:

$\Rightarrow v\propto \frac{1}{\sqrt{\mu }}\propto \sqrt{l}$

Since frequency is proportional to velocity which in turn is proportional to length, hence, ratio is $\frac{1}{\sqrt{\eta }}$.