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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 air as 344 m s^-1.

Q.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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Taking the speed of the sound in air as 344\ m/s.

Then,

we know: Speed = Wavelength\times Frequency

Or, v = \lambda \times \nu

Hence, 

For \nu =20\ Hz,

\lambda_{1} = \frac{v}{\nu_{1}} = \frac{344}{20} = 17.2\ m

and for \nu =20,000\ Hz

\lambda_{2} = \frac{v}{\nu_{2}} = \frac{344}{20,000} = 0.0172\ m

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

 

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