Question

In an experiment to determine the velocity of sound in air at room temperature using a resonance is observed when the air column has a length of $20.0$ cm for a tuning fork of frequency $400\, Hz$ is used. The velocity of the sound at room temperature is $336\, ms ^{-1}$. The third resonance is observed when the air column has a length of ______$cm$.

Answer 1

For first resonance
$\ell_{1}+ e =\frac{\lambda}{4}$
$\lambda=\frac{336}{400} \times 100\, cm =84\, cm$
$\Rightarrow \frac{\lambda}{4}=21\, cm$
$e =21-20=1\, cm$
For third resonance
$\ell_{3}+ e =\frac{5 \lambda}{4}=105\, cm$
$\Rightarrow \ell_{3}=104\, cm$