Answer to Question #3853 in Acoustics for mia

Question

The human ear can detect sounds with frequencies between 20 Hz and 16 kHz. Find the
greatest and the smallest wavelengths the ear can detect, assuming the sound travels.

Answer 1

The LENGTH of the WAVE is defined as distance between two next points of a sound wave which are in identical oscillatory position (have an identical phase).
The interrelation between length of a wave and frequency is defined by the following formula: λ = c / f , where "c" - speed of a sound in air, is usually used value of 330 (340) m/s. (The given value depends on temperature and humidity of air, and also from barometric pressure), and "f" - frequency in Hz.



16 kHz=16000Hz
The smallest wavelength λ_small = 330/16000 = 0.50625 m.
The greatest wavelength λ_great = 330/20 = 16.5 m.
The smallest wavelength is 0.020625 m.
The greatest wavelength is 16.5 m.