Sound Frequency, Wavelength and Octave

An introduction to the nature of sound with frequency, wavelength and octaves.

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 of one cycle for a 500 Hz tone can be calculated using (1):

T = 1 / (500 Hz) 

    = 0.002 s

The range for human hearing is from 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 an 0^oC the sound of speed 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.

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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