**Radian (rad)** a derived SI unit of angle measurement. One radian is the angle made at the centre of a circle by an arc whose length is equal to the radius of the circle.

Since the circumference of a circle = 2·π·r, then one radian equals 360°/(2·π) ≈ 57.3° and π/2 radians equals a right angle (90°)

To convert radians to degrees multiply the radians by 180/π : see also angles

**Radiation Index** IEC 801-31-27, in decibels, ten times the logarithm to the base ten of the *radiation factor*.

Indicators • LAeq,6h • LAeq,16h • LAeq,18h • Lday • Levening.

Random Incidence

**Random Incidence Microphone** also known as *diffuse field microphones*.

Because of their importance in acoustics we have a full page on measurement microphones

See also • free-field microphones • pressure microphones

**Random Noise Definition** IEC 801-21-09, oscillation due to the aggregate of a large number of elementary disturbances with random occurrence in time.

Other noise descriptors • ambient noise • background noise • broadband noise • gaussian noise • narrowband noise • periodic • pink noise • pseudo random noise • residual noise • specific noise • white noise • wideband noise

**Random Vibration** a vibration whose instantaneous amplitude is not specified at any instant of time.

Rapid Speech Transmission Index

**Ratio** the relative magnitudes of two quantities (usually expressed as a quotient)

Caution • Rayls may be in MKS and or CGS units, which are not the same.

**Rayleigh Disk** a disk on a torsion suspension designed to measure the sound particle velocity in a fluid.

Rayleigh Wave

**Reactance** the imaginary part of impedance.

See also • acoustic impedance

Reactive Sound Intensity

Reactive Sound Field

Reactivity Sound Index

**Real** (of a number or quantity) having no imaginary part.

**Real Time Analyser (RTA)** an instrument which uses a number of narrow bandwidth filters connected to a display to give a visual indication of the amplitude in each frequency band simultaneously or at the same time.

**Real Time Frequency Analysis** measurement of octave or third octave band noise where all the filters are measured simultaneously, ensures no loss of data.

**Real World +4 dB** in the real world there are factors that can reduce the effectiveness of hearing protectors: imperfect fitting and the condition of the protectors are two examples. To allow for this the *HSE - UK Government Health and Safety Executive* recommends the addition of 4 dB to the calculated level at the ear.

**Rectangular Window** a time window that has a zero value outside the specified time record and unity within the record length. In the FFT analyser, the rectangular window is actually no window at all. It is also called rectangular weighting, or uniform weighting, and is used when the signal to be analysed is a transient rather than a continuous signal : see also windowing.

**Reference Quantities** expressed in SI units

*Reference Particle Velocity (vo)* = 5 x 10^{-8} m/s ≡ 0 dB

*Reference Sound Energy (Wo)* = 10^{-12} J ≡ 0 dB

*Reference Sound Energy Density (wo)* = 1 pJ/m^{3} = 10^{-12} J/m^{3} ≡ 0 dB

*Reference Sound Exposure (Eo)* = (20 μPa)^{2} s ≡ 0 dB

*Reference Sound Intensity (Io)* = 1 pW/m^{2} = 10^{-12} W/m^{2} ≡ 0 dB

*Reference Sound Power (Po)* = 1 pW = 10^{-12} W ≡ 0 dB

*Reference Sound Pressure (po)* = 20 x 10^{-6} Pa ≡ 0 dB in air

*Reference Sound Pressure (po)* = 1 x 10^{-6} Pa ≡ 0 dB in liquids and solids

*Reference Vibratory Acceleration (ao)* = 1 μm/s^{2} ≡ 0 dB

*Reference Vibratory Displacement (ξo)* = 1pm ≡ 0 dB

*Reference Vibratory Force (Fo)* = 10^{-6} N ≡ 0 dB

*Reference Vibratory Velocity (vo)* = 1 nm/s ≡ 0 dB

*Reference Voltage (vo)* = 1 Volt ≡ 0 dB

See also our decibel reference tables

Reflected Sound Wave

Reflection

Refraction

Refraction Loss

**Residual Noise** the noise remaining when the specific noise is suppressed.

See also • background noise

**Resistance** the real part of impedance

See also • acoustic impedance

see also • anti-resonance

**Resonance Definition** IEC 801-24-05, phenomenon of a system in forced oscillation such that any change, however small, in the frequency of excitation results in a decrease in a response of the system

**Resonance Frequency Definition** IEC 801-24-06, frequency at which resonance exists

Reverberant Field

See also • anechoic

**Reverberation Room** IEC 801-31-13, room having a long reverberation time, especially designed to make the sound field therein as diffuse as possible

**Reverberation Time Definition** IEC 801-31-07, of an enclosure, for a sound of a given frequency or frequency band, time that would be required for the sound pressure level in the enclosure to decrease by 60 decibels, after the source has been stopped

**Sabine Reverberation Time Equation**, in 1898 W C Sabine also came up with the formulae relating
reverberation time with sound absorption and room volume: T = 0.161 V/A

where :

V = room volume in m^{3}

A = α x S = equivalent absorption surface or area in m^{2}

α = absorbent coefficient or attenuation coefficient

T = RT60 = reverberation time in s, seconds

S = absorbing surface in m^{2}

The above equation is normalized to the speed of sound in air = 343 m/s

It follows if you know the reverberation time you can calculate the absorption coefficient and vice-versa.

Measuring reverberation times also enables the calculation of the total sound absorption of a room. The reverberation time varies with frequency.

**Reverberation Time** is a significant parameter in acoustics : so we have more details

See also • artificial-reverberation • early decay time • schroeder • backward curve integration

**RMQ (Root Mean Quad)** is used in Vibration Dose VDV measurements to take account of the impulsive nature of these measurements. The procedure is similar to the more commonly used RMS method below except the 4th power average is calculated before taking the ∜ - quad root or 4th root.

**RMS (Root Mean Square of a time-varying quantity)** is obtained by squaring the amplitude at each instant, obtaining the average of the squared values over the interval of interest, and then taking the square root of this average.

**RMS Value Definition** IEC 103-02-03, for a time-dependent quantity, positive square root of the mean value of the square of the quantity taken over a given time interval

● Note : The abbreviation RMS was formerly denoted as r.m.s. or rms, but these notations are now deprecated.

*RMS Value* is also known as the effective value

The root-mean-square sound pressure, also known as the effective sound pressure is most often used to characterise a sound wave because it is directly related to the sound energy carried by a sound wave

See also • mean squareSee also other types of averaging

Indicators • LA10,18h • LAeq,16h • Lday • Levening.

Room Absorption

Room Absorption Coefficient

The changes are frequency dependent which makes things more complicated to predict. In large spaces air absorption can be significant at higher frequencies.

See also room modesThis system is considered by some to more effective than the noise criteria (NC) system.

The B&K 2250 sound analyser, measures RC values.

However rooms may also have one or more *modes* or
resonances related to the room dimensions and the
wavelength of the sound. These *room modes* and standing waves can dramatically effect the room's acoustic performance.

**Axial Modes** are associated with pairs of parallel walls.

**Tangential Modes** involve four room surfaces

**Oblique Modes** all six surfaces.

Root Mean Quad

Root Mean Square

Example 1: a *root power quantity* (sound pressure) of 1 pascal = 94 db SPL, add another identical sound source, the total = 2 pascals = 100 dB SPL. Two identical *root power* sources increase the sound pressure, a sound field quantity by 6 dB, i.e. 20 log (2) = 6dB. See our sound pressure table for more examples.

Example 2: a power quantity (sound power) of 1 Watt = 120 db SWL, add another identical sound source, the total = 2 Watts = 123 dB SWL. Two identical power sources increase the sound power output by 3 dB, i.e. 10 log (2) = 3 dB. See our sound power table for more examples.

See also our sound level calculation page and the IEC decibel definition.**rpm •** revolutions per minute

*RT •* reverberation time

*RT60 •* reverberation time

*Rw •* weighted sound reduction index

*R'w •* weighted apparent sound reduction index