Question

A person has a hearing range from 20 hz to 20khz . 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​

Answer 1

$\large \sf{ \color{blue}{Question}}$

A person has a hearing range from 20 hz to 20khz . 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

$\sf \large{ \color{blue}{Solution}}$

In the first case :

$\implies\bold{ \color{darkblue}{speed \: (v) \: = \: 344 \: {ms}^{2} }}$

$\implies\bold{ \color{darkblue}{frequency \:(f) \: = 20 \: hz}}$

$\implies\bold{ \color{darkblue}{wavelength \: \lambda = ?}}$

Now, we know that

$\implies\bold{ \color{darkblue}{v \: = \: f \: \times \: \lambda}}$

$\implies \bold{ \color{darkblue}{344 = f \times \lambda}}$

$\implies \bold{ \color{darkblue}{ \lambda = \frac{344}{20} }}$

$\bold{ \color{darkblue}{wavelenth \: \lambda \: = 17.2m}}$

Now , In second case :

$\implies\bold{ \color{darkblue}{speed \: (v) \: = \: 344 \: {ms}^{2} }}$

$\implies\bold{ \color{darkblue}{frequency \:(f) \: = 20 \: khz}}$

$\bold{ \color{darkblue}{ = 20 \times 1000 \: hz}} \\ \bold{ \color{darkblue}{ = 20000 \: hz}}$

$\bold{ \color{darkblue}{wavelenth \: \: \lambda \: = ?}}$

$\implies\bold{ \color{darkblue}{v \: = \: f \: \times \: \lambda}}$

$\implies \bold{ \color{darkblue}{344 = 20000\times \lambda}}$

$\implies \bold{ \color{darkblue}{ \lambda = \frac{344}{20000} }}$

$\bold{ \color{darkblue}{wavelenth \: \lambda \: = 0.0172m}}$

Thus, the wavelength of sound in air corresponding to the frequencies of 20 Hz and 20KHz are 17.2m and 0.0172m respectively

Answer 2

wavelenth λ=0.0172m.

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