# Sound - Frequency, Wavelength and Octave

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 ^{ 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

### Air - Speed of Sound vs. Temperature

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.

### 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 - 212°F (0 - 100°C) - Imperial and SI units.