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# 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 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 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.

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