Question

Calculate the frequency of beats produced in air when two sources of sound are activated, one emitting a wavelength of 32 cm and the other of 32.2 cm. The speed of sound in air is 350 m s⁻¹.

Answer 1

For source A :
Wavelength \[\lambda\] = 32 cm = 32\[\times\]`10^\{-}`² m
Velocity v = 350 `ms^(-1)`

Frequency \[\left( n_1 \right)\] is given by : 

\[ n_1  = \frac{v}{\lambda} = \frac{350}{32 \times {10}^{- 2}} = 1093 . 75  \text { Hz }\]

For source B:   
Velocity v = 350 ms⁻¹
Wavelength \[\lambda\] = 32.2 cm = 32.2\[\times\] `10^\(-)`² m

Frequency \[\left( n_2 \right)\] is given by : 

\[ n_2  = \frac{v}{\lambda} = \frac{350}{32 . 2 \times {10}^{- 2}} = 1086 . 96 \text {  Hz }\]

∴ Beat frequency =  1093.75 − 1086.96 = 6.79 Hz \[\approx\] 7 Hz