Question

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 20cm and 73cm column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at 27°C is: -
(1) 330m/s
(2) 339m/s
(3) 350m/s
(4) 300m/s

Answer 1

Hint: The frequency is the characteristic of the source and it does not change. The velocity of the sound is dependent upon the medium as it is a longitudinal wave. Here we can exploit the relationship between frequency, velocity and Time period.

Complete step by step answer:
We are not given that any gas is present in the glass tube or not, so, air is present there and we know that the velocity of sound in air at 27°C is 339m/s. Given that two successive resonance is produced, so using the formula of resonance: \[V=2f({{l}_{2}}-{{l}_{1}})\]
$
V=2\times 320(0.73-0.2) \\
\implies V=640\times 0.53 \\
\therefore V=339.2m/s \\
$

So, the correct answer is “Option 2”.

Additional Information:
The vibrating object is the source of the disturbance that moves through the medium and when such a body vibrates which is to and fro motion it happens at a particular frequency.

Note:
We know that a closed end tube resonates if the length of the tube is one fourth the wavelength of the sound. While on the other hand a closed end tube only resonates on the odd harmonics. Also, speed of sound depends upon the medium of travelling.