Question

2.
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 27°C 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 27°C is
[NEET-2018]
(2) 339 m/s
(1) 330 m/s
(4) 350 m/s
(3) 300 m/s​

Answer 1

$\large{\bf{\gray{\underline{\underline{\orange{Given:}}}}}}$

At room temperature of 27°C, Two successive resonances are produced at 20cm and 73cm in glass tube.

Frequency of the tuning fork = 320Hz

$\large{\bf{\gray{\underline{\underline{\green{To\:Find:}}}}}}$

We have to find speed of sound in air at 27°C.

$\large{\bf{\gray{\underline{\underline{\pink{Solution:}}}}}}$

For first resonance,

$:\implies\tt\:l_1=\dfrac{\lambda}{4}\:\longrightarrow\:(i)$

For second resonance,

$:\implies\tt\:l_2=\dfrac{3\lambda}{4}\:\longrightarrow\:(ii)$

Subtract (i) from (ii), we get

$:\implies\tt\:(l_2-l_1)=\dfrac{3\lambda}{4}-\dfrac{\lambda}{4}$

$:\implies\bf\:\lambda=2(l_2-l_1)\:\longrightarrow\:(iii)$

Velocity of sound wave is given by,

$:\implies\tt\:v=\nu\lambda$

where, $\nu$ is the frequency.

$\circ\tt\:v=\nu[2(l_2-l_1)]\:[\sf{from\:Eq.\:(iii)}]$

$\circ\tt\:v=320[2(0.73-0.20)]$

$\circ\tt\:v=640\times 0.53$

$\dag\:\boxed{\bf{\purple{v=339\:ms^{-1}}}}$