Question

A sound of wavelength 0.332m has a time period of 10 -3 s .If the time period is decreased to 10-4 calculate wavelength and frequency of the new wave.

Answer 1

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• $\boxed{λ_{2} = 0.0332m, v_{2 } = {10}^{4} Hz}$

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Speed(v), wavelength(λ), and Time period(T) of sound wave are related as

$\to v = \frac{λ}{T}$

Thus, wavelength and time period of the two sound waves are related as

$\to \frac{λ_{1}}{T_{2}} = v = \frac{λ_{2}}{T_{2}}$

$\to \frac{0.332}{{10}^{-3}} = \frac{λ_{2}}{{10}^{-4}}$

$\to \frac{0.332\times {10}^{-4}}{{10}^{-3}} = λ_{2}$

$\to λ_{2} = 0.0332m$

Frequency of a sound wave is given by

$\to ν_{2 } = \frac{1}{T_{2} }$

$\to v_{2 } = \frac{1}{{10}^{-4}}$

$\to v_{2 } = {10}^{4} Hz$