**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

**Radian per second (rad/s)** see angular velocity

Random Incidence

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

Used for measurements in reflective room and chambers as opposed to the Free-field Microphones, used for measurements in more open spaces. The presence of the microphone should not to effect the measurement.

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

See also • free-field microphones • pressure microphones

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)

**Rayl** a unit of specific acoustic impedance, the ratio of the sound pressure to the particle velocity - named after Lord Rayleigh.

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 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.

See also our decibel reference tables

Reflected Wave

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

● Note : the quantity that is the measure of response should be indicated; for example, velocity resonance.

● Note : in case of possible confusion, the type of resonance must be indicated; for example, velocity resonance frequency.

Reverberant Field

● Note : Reverberation rooms are used in particular for the measurement of absorption coefficients of materials and of the sound power of sound sources

**Sabine's 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. For a
sine wave, if you multiply the RMS value by the square root of 2 (1.414), you get the peak value of the wave.

● Note : The root-mean-square value of a quantity may be denoted by adding one of the subscripts eff or rms to the symbol of the quantity

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

**RMS Averaging** also called *power spectrum averaging*, calculates the weighted average of the sum of the squared levels. The weighting is either linear or exponential. *RMS averaging* reduces random fluctuations in the levels but does not reduce the noise floor.

See also other types of averaging

Room Absorption

Room Absorption Coefficient

**Room Acoustics** sound waves are reflected by the walls, ceiling, floor and any object they come into contact with. The reflected wave is modified in various ways. sound absorption is a major contributor, hard reflecting surfaces common in reverberant rooms leave the sound largely unchanged whereas soft absorbent surfaces found in the home produce significant changes.

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

**Room Criteria (RC)** a single-number for rating room noise. Based on the preferred speech interference level values. Suffixes are added, R for Rumble, RV for Vibration and Rattle, H for Hiss and N for Neutral.

This system is considered by some to more effective than the Noise Criteria (NC) system.

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

**Room Modes** when sound is generated in a room, by a loudspeaker for example, the sound 'decays' in time due to the sound interacting with the room surfaces and objects in the room see sound absorption. The time taken for the sound to decay is known as the reverberation time.

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

Root Mean Quad

Root Mean Square

Example 1: a sound source of 1 pascal = 94 db SPL, add another identical sound source, total = 2 pascals = 100 dB SPL. Two identical source increase the sound pressure, a sound field quantity by 6 dB. 20 log(2) = 6dB

Example 2: a sound source of 1 Watt = 120 db SWL, add another identical sound source, total = 2 Watts = 123 dB SWL. Two identical sources increase the sound power output by 3 dB. 10 log(2) = 3dB

10 dB is a 10x change in *power quantities * and 20x change in *field quantities*

**rpm** ▷ revolutions per minute

*RT* ▷ reverberation time

*RT60* ▷ reverberation time

*Rw* ▷ weighted sound reduction index

*R'w* ▷ weighted apparent sound reduction index

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