Question

Consider the following statements regarding the experiment to the determine the velocity of sound in laboratory by resonance tube method.
1. The first resonance is obtained for the length $x_1$ of the air column
2. The second resonance is obtained for the length $x_2$ of the air column.
If $n$ be the frequency of the tuning fork then which is the correct relation ($v$ represents the velocity of sound) ?

• A. $v=2n(x_1+x_2)$
• B. $v=2n(x_1-x_2)$
• C. $v=2n(x_2-x_1)$
• D. $v=2n\left(x_1{x}_2\right)$

Answer 1

The correct option is C $v=2n(x_2-x_1)$

Frequency in a resonant tube=$f=p\frac{v}{2l}$

where $p$ is for the pth harmonic.

Thus $n=\frac{v}{2x_1}$

and $n=2\frac{v}{2x_2}$

$⟹v=2n(x_2-x_1)$