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Sound Frequency, Wavelength and Octave
An introduction to the nature of sound - frequency, wavelength and octaves
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Sound energy is transmitted through air (or other particles) as a traveling pressure wave. In air the displacement wave amplitude may range from 10-7 mm to a few mm per second.
Frequency
The frequency - cycles per second - of a sound is expressed in hertz - Hz. The frequency can be expressed as
f = 1 / T (1)
where
f = frequency (s-1, Hz)
T = time for completing one cycle (s)
Example - Frequency
The time for completing one cycle for a 500 Hz tone can be calculated using (1) as
T = 1 / (500 Hz)
= 0.002 s
The range for human hearing is 20 to 20.000 Hz. By age 12-13.000 Hz are the upper limit for many people.
Wavelength
The wavelength of sound is the distance between analogous points of two successive waves.
λ = c / f (2)
where
λ = wavelength (m)
c = speed of sound (m/s)
f = frequency (s-1, Hz)
Example - the Wavelength of a Tone
In air at normal atmosphere at 0 oC the speed of sound is 331.2 m/s. The wavelength of a 500 Hz tone can be calculated as:
λ = (331.2 m/s) / (500 Hz)
= 0.662 m
Octave
An octave is the interval between two points where the frequency at the second point is twice the frequency of the first.
| Octave | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Frequency (Hz) | 63 | 125 | 250 | 500 | 1K | 2K | 4K | 8K |
| Wavelength in air (70oF, 21oC) (ft) |
17.92 | 9.03 | 4.52 | 2.26 | 1.129 | 0.56 | 0.28 | 0.14 |
| Wavelength in air (70oF, 21oC) (m) |
5.46 | 2.75 | 1.38 | 0.69 | 0.34 | 0.17 | 0.085 | 0.043 |
A musical tone is eight full tones above or below an another tone, with twice or half as many vibrations per second as the other tone.
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