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

0.017 m - 17 m

Step-by-step explanation:

The relationship between wavelength and frequency of a wave is:

`\lambda=(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=(340 m/s)/(20 Hz)=17 m`

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

`\lambda=(340 m/s)/(20,000 Hz)=0.017 m`