Question.
A person has a hearing range from $20 \mathrm{~Hz}$ to $20 \mathrm{kHz}$. What are the typical wavelengths of sound waves in air corresponding to these two frequencies? Take the speed of sound in air as $344 \mathrm{~ms}^{-1}$.
A person has a hearing range from $20 \mathrm{~Hz}$ to $20 \mathrm{kHz}$. What are the typical wavelengths of sound waves in air corresponding to these two frequencies? Take the speed of sound in air as $344 \mathrm{~ms}^{-1}$.
Solution:
Given, speed of sound, $\mathrm{v}=344 \mathrm{~ms}^{-1}$
For frequency $v_{1}=20 \mathrm{~Hz}$, wavelength, $\lambda_{1}=?$
Wavelength of sound of frequency $20 \mathrm{~Hz}$
$\lambda_{1}=\frac{v}{v_{1}}=\frac{344}{20}=17.2 \mathrm{~m}$
For frequency $v_{2}=20 \mathrm{kHz}=20000 \mathrm{~Hz}$,
wavelength, $\lambda_{2}=?$
$\lambda_{2}=\frac{v}{v_{2}}=\frac{344}{20000}=1.72 \times 10^{-2} \mathrm{~m}$
Given, speed of sound, $\mathrm{v}=344 \mathrm{~ms}^{-1}$
For frequency $v_{1}=20 \mathrm{~Hz}$, wavelength, $\lambda_{1}=?$
Wavelength of sound of frequency $20 \mathrm{~Hz}$
$\lambda_{1}=\frac{v}{v_{1}}=\frac{344}{20}=17.2 \mathrm{~m}$
For frequency $v_{2}=20 \mathrm{kHz}=20000 \mathrm{~Hz}$,
wavelength, $\lambda_{2}=?$
$\lambda_{2}=\frac{v}{v_{2}}=\frac{344}{20000}=1.72 \times 10^{-2} \mathrm{~m}$
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