Bobby Gross

2023-02-22

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 $344\frac{m}{s}$.

Michaela Perez

Given data
The person's capacity for hearing$=20Hz-20KHz$
Speed of sound in air $=$$344\frac{m}{s}$
Formula used
Speed $=$ Frequency$×$Wavelength
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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