Question

The human ear can detect continuous sounds in the frequency range from 20 Hz to 20,000 Hz. Assuming that the speed of sound in air is 330 ms1 for all frequencies; calculate the wavelengths corresponding to the given extreme frequencies of the audible range

Answer 1

Audible range of hearing for a normal human ear is 20 Hz to 20,000 Hz.

Speed of sound in air, v = 330 ms^-1

Speed, wavelength and frequency are related as

v = nλ

`:. lambda = v/n`

n_lower = 20 Hz

n_upper  = 20,000 Hz

`:. lambda_"lower" = v/(n_"lower")`

`:.lambda_"lower" = 330/20 = 16.5 m`

Similary `lambda_"upper" = v/n_"upper"`

`:. lambda_"upper" = 330/20000` = 0.0165 m = 16.5 mm