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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.

Sound 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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