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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.
Solution
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
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