Question

A tuning fork of frequency $f$ resonates with a closed organ pipe when the length of the shortest air columns are $a$ and $b$ respectively. the speed of sound in air is

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

Answer 1

Answer: (C)

$2f(b-a)$

Speed of sound in air and length of the pipe are represented by $v$ and $L$ respectively.

Frequency of different modes of vibration in a closed organ pipe, ${\nu }_n=\frac{(2n-1)v}{4L}$

For length of the pipe to be $a$, $f=\frac{(2n-1)v}{4a}$

$⟹(2n-1)v=4af$ ...................(1)

For length of the pipe to be $b$, $f=\frac{\left(2\right[n+1]-1)v}{4b}$

$f=\frac{(2n+1)v}{4b}$

$⟹(2n+1)v=4bf$ ...........(2)

Subtracting (1) from (2), $2v=4bf-4af$

$⟹v=2f(b-a)$