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 $400Hz$ is used. The velocity of the sound at room temperature is $336m{s}^{-1}$. The third resonance is observed when the air column has a length of ______$cm$.

Answer 1

Answer: 104

For first resonance
${\ell }_1+e=\frac{\lambda }{4}$
$\lambda =\frac{336}{400}\times 100cm=84cm$
$\Rightarrow \frac{\lambda }{4}=21cm$
$e=21-20=1cm$
For third resonance
${\ell }_3+e=\frac{5\lambda }{4}=105cm$
$\Rightarrow {\ell }_3=104cm$