Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Sound - Frequency, Wavelength and Octave

An introduction to the nature of sound with frequencies, wave-lengths and octaves.

Sponsored Links

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, 1/s, Hz)

T = time for completing one cycle (s)

Example - Frequency 

The time for completing one cycle for a 500 Hz tone can be calculated as

T = 1 / (500 Hz) 

    = 0.002 s

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

Example - Parallel to Alternating Current

An alternating current completes 5 cycles in 100 ms.

The time for completing one cycle can be calculated

T = (100 ms/cycle) / (5 cycles)

  = 20 ms

The frequency of the alternating current can be calculated as

f = 1 / ((20 ms) (10-3 s/ms))

  = 50 Hz

Wavelength

The wavelength of sound is the distance between the 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 and 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
Sponsored Links

Related Topics

Related Documents

Sponsored Links

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro .Add the Engineering ToolBox extension to your SketchUp from the SketchUp Pro Sketchup Extension Warehouse!

Translate
About the Engineering ToolBox!

Privacy

We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

Google use cookies for serving our ads and handling visitor statistics. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected.

AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information.

Citation

This page can be cited as

  • Engineering ToolBox, (2003). Sound - Frequency, Wavelength and Octave. [online] Available at: https://www.engineeringtoolbox.com/sound-frequency-wavelength-d_56.html [Accessed Day Mo. Year].

Modify access date.

. .

close

3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Scientific Online Calculator

Scientific Calculator

3 10

Sponsored Links
.