Sound Frequency, Wavelength and Octave

An introduction to the nature of sound - 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 for completing one cycle for a 500 Hz tone can be calculated using (1) as

T = 1 / (500 Hz) 

    = 0.002 s

The frequency range for human hearing is 20 to 20.000 Hz. By age the upper limit for many is 12-13.000 Hz.

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
Center Frequency
(Hz)
31.25 62.5 125 250 500 1000 2000 4000 8000 16000
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

Although the octave is the eighth note of a series in any key - an octave is separated by 5 whole notes and 2 half notes.

  • only six whole notes separates an octave

Example - Guitar

A guitar's open E string ascends by whole notes as

  • E F# G# A# C D E
  • 1 2 3 4 5 6

Related Topics

  • Acoustics - Room acoustics, acoustic properties - decibel A, B and C - Noise Rating (NR) curves, sound transmission, sound pressure, sound intensity, attenuation and more
  • Noise and Attenuation - Noise is usually defined as unwanted sound - noise, noise generation, silencers and attenuation in HVAC systems

Related Documents

Key Words

  • en: sound noise wavelength octave frequency
  • es: ruido sonido de octava de longitud de onda
  • de: Schallgeräusche Wellenlänge Oktave Frequenz

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