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# Answer to Question #3853 in Acoustics for mia

Question #3853
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.
1
2011-08-25T13:35:35-0400
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: &lambda; = c / f , where &quot;c&quot; - 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 &quot;f&quot; - frequency in Hz.

16 kHz=16000Hz
The smallest wavelength &lambda;small = 330/16000 = 0.50625 m.
The greatest wavelength &lambda;great = 330/20 = 16.5 m.
The smallest wavelength is 0.020625 m.
The greatest wavelength is 16.5 m.

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