Question

# A person has a hearing range from $20Hz$ 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 $344\frac{m}{s}$.

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Solution

## Step 1: Given dataThe hearing range of the person $=20Hz-20KHz$Speed of sound in air $=$$344\frac{m}{s}$Step 2: Formula usedSpeed $=$ Frequency$×$WavelengthStep 3: Solution$v=f×\lambda$(i). For the frequency $f=20Hz$$⇒\lambda =\frac{344}{20}=17.2m$(ii). For the frequency $f=20kHz$$⇒\lambda =\frac{344}{20×{10}^{3}}=0.0172m$Hence, the range of wavelength is $0.0172m-17.2m$.

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