Question

A string of length $l$ hangs freely from a rigid support. The time required by a transverse pulse to travel from bottom to top of the string is

• A. $\sqrt{lg}$
• B. $\sqrt{\left(l/g\right)}$
• C. $\sqrt{2l/g}$
• D. $2\sqrt{\frac{l}{g}}$

Answer 1

The correct option is D $2\sqrt{\frac{l}{g}}$

$f=\frac{\nu }{2l}=\frac{\sqrt{\frac{T}{m/l}}}{2l}=\frac{1}{2}\sqrt{\frac{T}{ml}}=\frac{1}{2}\sqrt{\frac{mg}{ml}}$
$=\frac{1}{2}\sqrt{\frac{g}{l}}$
time taken $=\frac{1}{f}=2\sqrt{\frac{l}{g}}.$