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
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
-
Air - Speed of Sound vs. Temperature
Speed of sound in air at standard atmospheric pressure with temperatures ranging -40 to 1000oC (-40 to 1500oF) - Imperial and SI Units. -
Decibel A, B and C
Sound pressure filters that compensates for the hearing sensed by the human ear. -
Electromagnetic Spectrum
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. -
Noise Rating (NR) - Free Online Calculator
An online Noise Rating (NR) calculator. -
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. -
RC - the Room Criteria
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. -
Sound Pressure
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 - 212oF (0 - 100oC) - Imperial and SI units.
