Question

A tuning fork of frequency v resonates with a closed organ pipe when the lengths of the shortest air columns are a and b respectively. The speed of sound in air is :

• A. $v(a-b)$
• B. $v\frac{(b-a)}{2}$
• C. $2v(b+a)$
• D. $2v(b-a)$

Answer 1

The correct option is D $2v(b-a)$

Frequency at $n^t$ overtone is $f_1=\frac{n}{2l}\sqrt{\frac{T}{\mu }}$

$l=\frac{n}{2f}\sqrt{\frac{T}{\mu }}$

$l_1-l_2=\frac{V}{2f}=(b-a)$

$\therefore velocity,V=2f(b-a)$