Sound  Frequency, Wavelength and Octave
An introduction to the nature of sound with frequencies, wavelengths 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}, 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 1213.000 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.
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^{ o}C 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 (70^{o}F, 21^{o}C) (ft) 
17.92  9.03  4.52  2.26  1.129  0.56  0.28  0.14  
Wavelength in air (70^{o}F, 21^{o}C) (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
Related Topics

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

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Speed of sound in air at standard atmospheric pressure with temperatures ranging 40 to 1000 °C (40 to 1500 °F)  Imperial and SI Units. 
Decibel A, B and C
Sound pressure filters that compensates for the hearing sensed by the human ear. 
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The electromagnetic spectrum with wavelengths and frequencies. 
Maximum Sound Pressure Levels in Rooms
Maximum recommended sound pressure levels in rooms like kindergartens, auditoriums, libraries, cinemas and more. 
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Notes, Octaves and Frequencies
Frequencies vs. notes and octaves. 
NR  the Noise Rating Curve
The Noise Rating (NR) Curve used to determine acceptable indoor environments for hearing preservation, speech communication and annoyance. 
Octave Band Frequencies
The octave and the 1/3 octave band frequencies. 
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The Room Criteria (RC) is used to measure background noise in buildings for frequencies ranging 16 to 4000 Hz. 
Sound  Attenuation and Speed vs. Sound Frequency and Air Humidity
The speed and attenuation of sound in moist air varies with sound frequency and air humidity. 
Sound  Hearing Threshold vs. Age
Shift in hearing threshold for men and women vs. age. 
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Sound Pressure is the force of sound on a surface perpendicular to the propagation of sound. 
Speed of Sound vs. Elevation, Temperature and Air Pressure
Altitude and speed of sound, temperature and pressure. 
Water  Speed of Sound vs. Temperature
Speed of sound in water at temperatures ranging 32  212°F (0  100°C)  Imperial and SI units.