# 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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Given:
A person has a hearing range from $20\ Hz$ to $20\ kHz$.

To do:
To find out the typical wavelengths of sound waves in air corresponding to the above given two frequencies.

Solution:
To find out the typical wavelengths of sound waves in air corresponding to these two frequencies, let us know the relation between the speed, frequency, and wavelength of a sound wave:

Relation between the speed, frequency, and wavelength:

$\boxed{Speed(v)=Wavelength(\lambda)\times Frequency(f)}$

Given that the speed of sound in air$=344\ m/s$

By using the above relation, we can now find out the wavelengths of a sound wave in air with the corresponding frequencies.

$(i)$. Wavelength of the sound wave when the frequency is $20\ Hz$:

$\lambda_1=\frac{v}{f}$

Or $\lambda_1=\frac{344}{20}$

Or $\lambda_1=17.2\ m$

$(ii)$.  Wavelength of the sound wave when the frequency is $20000\ Hz$:

$\lambda_2=\frac{v}{f}$

$\lambda_2=\frac{344}{20000}$

Or $\lambda_2=0.172\ m$

Hence, for humans, the wavelength range for hearing is $0.0172\ m$ to $17.2\ m$.
Updated on 10-Oct-2022 13:23:15