Question

Wavelengths of two notes in the air are`[70/153]^m` and `[70/157]^m`. Each of  these notes produces 8 beats per second with a tuning fork of fixed frequency. Find the velocity of sound in the air and frequency of the tuning fork.

Answer 1

Let the wavelength of the tuning fork be L

∴ f = c/L

given,

c/(70/157) - c/L = 8

∴ 157c/70 - c/L = 8 ... (1)

and,

c/L - c/(70/153) = 8

∴ c/L - 153c/70 = 8 ... (2)

adding 1 and 2

(157c - 153c)/70 = 16

∴ 4c = 1120

∴ c = 280 m/s

as f = c/L

∴ f = 280/L

substituting in (1)

157 × 280/70 - f = 8

f = 628 - 8

∴ f = 620Hz