Question

A string of length $L$ and mass $M$ hangs freely from a fixed point. Then, the velocity of transverse waves along the string at a distance $x$ from the free end is

• A. $gx$
• B. $\sqrt{gx}$
• C. $gL$
• D. $\sqrt{gL}$

Answer 1

The correct option is B $\sqrt{gx}$

Total length of string $=L$
Mass of the string $=M$
The velocity of transverse wave $v=\sqrt{\frac{T}{m}}$
where, $T=$ weight of part of string hanging below the point under consideration
$=\left(\frac{M}{L}\right)xg$
$\Rightarrow v=\sqrt{\frac{\left(\frac{M}{L}\right)xg}{\left(\frac{M}{L}\right)}}=\sqrt{xg}$