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Question
A person can hear sound waves in the frequency range 20 Hz to 20 kHz. Find the minimum and the maximum wavelengths of sound that is audible to the person. The speed of sound is 360 m s−1.
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Solution
Given:
Speed of sound v = 360 ms−1
(a) We know that frequency \[\propto \frac{1}{\text { Wavelength }}\]
Therefore, for minimum wavelength, the frequency f = 20 kHz.
We know that v = fλ.
\[\therefore \lambda = \frac{360}{\left( 20 \times {10}^3 \right)}\]
\[ \Rightarrow \lambda = 18 \times {10}^{- 3} m = 18 \text { mm }\]
(b) For maximum wave length:
\[\text { Frequency } f = 20 Hz\]
\[v = f\lambda\]
\[ \therefore \lambda = \frac{v}{f}\]
\[ \Rightarrow \lambda = \frac{360}{20} = 18 \text { m }\]
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