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

34.4 m; 3.44 c m

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17.2 m; 1.72 c m

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1.72 m; 17.2 m

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3.44 c m; 34.4 m

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Solution

The correct option is B $17.2 m; 1.72 c m$
Hearing range $= 20 H z$ to $20 k H z (= 20000 H z)$

Speed of sound in the air $= 344 m s^{- 1}$

For a wave, Wavelength $=$ velocity/frequency.

For, $v = 20 H z = 20 s^{- 1}$

$λ = 344 / 20 = 17.2 m$

For, $v = 20000 H z = 20000 s^{- 1}$

$λ = 344 / 20000 = 0.0172 m = 1.72 c m$

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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 the air as 344 ms−1.

The correct option is B 17.2 m ; 1.72 cmHearing range =20 Hz to 20 kHz (=20000 Hz) Speed of sound in the air =344 ms−1 For a wave, Wavelength = velocity/frequency. For, v=20 Hz=20s−1 λ=344/20=17.2 m For, v=20000 Hz=20000 s−1 λ=344/20000=0.0172 m=1.72 cm

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