Question 7
A person has a hearing range from 20 Hz to 20 kHz. What are the typical wavelengths of sound waves in air corresponding to these two frequencies? Take the speed of sound in air as $344 m s^{- 1}$ .

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Solution

For a sound wave,
Speed = Wavelength $\times$ Frequency
$V = λ \times f$
Speed of sound in air = 344 m/s (Given)

(i) For, f = 20 Hz
$λ_{1} = \frac{V}{f} = \frac{344}{20} = 17.2 m$

(ii) For, f = 20000 Hz
$λ_{2} = \frac{V}{f} = \frac{344}{20000} = 0.0172 m$

Hence, for humans, the wavelength range for hearing is 0.0172 m to 17.2 m.

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Perception of Sound

Standard X Physics

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Question 7 A person has a hearing range from 20 Hz to 20 kHz. What are the typical wavelengths of sound waves in air corresponding to these two frequencies? Take the speed of sound in air as 344ms−1.

For a sound wave, Speed = Wavelength × Frequency V=λ×f Speed of sound in air = 344 m/s (Given) (i) For, f = 20 Hz λ1=Vf=34420=17.2m (ii) For, f = 20000 Hz λ2=Vf=34420000=0.0172m Hence, for humans, the wavelength range for hearing is 0.0172 m to 17.2 m.

Question 7
A person has a hearing range from 20 Hz to 20 kHz. What are the typical wavelengths of sound waves in air corresponding to these two frequencies? Take the speed of sound in air as $344 m s^{- 1}$ .