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

CONCEPT:

The frequency is the characteristic of the source and velocity is dependent upon the medium as a longitudinal wave. Therefore we can use the formula of resonance written as;

v = 2f [L2 - L1] ----(1)

Here, v is the velocity of the sound in air, f is the frequency, and L₁, L₂ is the length of a glass tube.

CALCULATION:

Given: L₂  = 73 cm

L₁  = 20 cm

f = 320 Hz

Now, by using equation (1) we get;

v = 2 f [L₂ - L₁]

⇒v = 2 × 320 [73 - 20] × 10^-2 

⇒ v = 339.2 ms^-1

⇒ v = 339 m/s

Hence, option 1) is the correct answer.