Question

What range of sound wavelengths in air at room temperature are audible to a human with ideal hearing (f= 20 Hz - 20 kHz)?

Answer 1

Answer:

0.017 m - 17 m

Explanation:

The relationship between wavelength and frequency of a wave is:

$\lambda=\frac{v}{f}$

where v is the speed of the wave, $\lambda$ the wavelength and f the frequency.

The speed of sound waves in air at room temperature is

v = 340 m/s

For the lowest frequency, f = 20 Hz, the wavelength is

$\lambda=\frac{340 m/s}{20 Hz}=17 m$

For the highest frequency, f = 20 kHz = 20,000 Hz, the wavelength is

$\lambda=\frac{340 m/s}{20,000 Hz}=0.017 m$