A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of 27⁰C, two successive resonances are produced at 20 cm and 73 cm of column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at 27⁰ C is 

For first resonance,  $l_1=\frac{\lambda }{4}$

For second resonance,  $l_2=\frac{3\lambda }{4}$

$\therefore \left(l_2-l_1\right)=\frac{3\lambda }{4}-\frac{\lambda }{4}$

or    $\lambda =2\left(l_2-l_1\right)$    …(i)

As, velocity of sound wave is given as 

$v=v\lambda$

where, $\nu$ is the frequency. 

$\Rightarrow v=v\left[2\left(l_2-l_1\right)\right]$                   …(ii)

[ From Eq. (i)]

Here, $\nu$ = 320 Hz

          $l_2=0.73\mathrm{m},l_1=0.20\mathrm{m}$     (Given)

Putting the values in Eq. (ii), we get 

$v=320\left[2\right(0.73-0.20\left)\right]=2\times 320\times 0.53$

$=339.2{\mathrm{ms}}^{-1}\simeq 339{\mathrm{ms}}^{-1}.$