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Question

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.


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Solution

Step 1- Given data

The speed of sound in air v=344m/s

Hearing range i.e. 20Hzto20kHz

Step 2- Finding wavelength regarding 20 Hz frequency

For a sound wave-

Speed (ν ) = Wavelength (λ) x Frequency(f)

v=f1λ1

f1=20Hzλ1=vf1λ1=34420λ1=17.2m

Step 3- Finding wavelength regarding 20 kHz frequency

v=f2λ2

λ2=vf2λ2=34420000λ2=0.0172m

Hence, for humans, the wavelength range for hearing is0.0172mto17.2m.


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