Sound - Frequency, Wavelength and Octave
An introduction to the nature of sound with frequencies, wave-lengths 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 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.
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