Reverberation Time

Reverberation Time is calculated using a linear least-squares regression of the actual measured decay curve. In simple terms, the calculation finds the straight line (linear fit) that best fits as a representation of all the measured data.

The XL2 automatically calculates two auxiliary results, correlation and uncertainty. These are both required by the standards, and indicate the precision of the results.

Correlation indicates how well the calculated linear fit matches to the actual decay curve. A high correlation value indicates a linear, non-distorted decay curve.
The correlation factor is expressed as a percentage; 100% represents perfectly linear sound pressure level decay after the sound source has ceased. The natural deviation from this linearity results in lower correlation values. Actual correlation factors are typically between 80 and 100%.
Uncertainty is introduced because pink noise is not a consistent signal, rather a random signal. It depends on the reverberation time (longer times produce lower uncertainty) and the bandwidth of the individual frequency band (broader bandwidth produces lower uncertainty). Also, lower bands show a higher uncertainty factor.

Uncertainty is influenced by the number of test cycles, the measurement method (T20 or T30), and the measurement filter (1/3rd or 1/1 octave resolution).

So, for a lower uncertainty (i.e. a better measurement accuracy),

T30 is better than T20
1/1 octave measurements are better than 1/3rd measurements
5 cycles is better than 3
(Note: a minimum of 3 cycles is required)
Use more measurement positions in the room

It is recommended to place the sound source and the microphone in multiple positions, and average all the readings, to compensate, for example, for any room modes (resonances brought about by the dimensions of the room).

The microphone should always be placed at least 1 meter from reflecting surfaces (walls, doors, windows, floors, tables).

Further, there is a formula that helps us determine where to place the microphone relative to the sound source. It gives us the minimum distance required between any source of sound and the measurement microphone for a valid reverberation time measurement. This is known as the critical distance.

RT60 Critical Distance formula

Dc = critical distance [m]

V = Volume of the room [m3]

C = Speed of sound [m/s]

T = Expected Reverberation Time for the room [s]

Example: in a small hall, at a room temperature of 20℃, with dimensions of 10 meters by 9 meters and a height of 5 meters, and an expected Reverberation Time of 2 seconds, the microphone must be at least 1.6 meters away from the sound source.

V = 10 * 9 * 5 = 450 m3

C = 342 m/s (the speed of sound @ 20℃)

T = 2 seconds

Critical Distance Dc = 2 *√ (450 / (342 * 2)) = 1.6 meters

The XL2 Acoustic Analyzer measures the Reverberation Time with 1/1 octave resolution, or, with the addition of the Extended Acoustic Pack Option, with 1/3rd octave resolution.

For many applications, using a 1/1 octave resolution is sufficient, unless the specification documentation with which you are working requires a 1/3rd octave resolution.

Typically, the ambient noise in a room (e.g. an apartment or office) would create a noise floor of 40-50 dB. To measure a decay of 60 dB from a sound source, we have to inject the sound at 75 dB (with 5 dB for the auto trigger and 10 dB headroom to the noise floor) above this noise floor. Creating such sound at 125 dB across the whole spectrum, and particularly at low frequencies, requires awfully high sound pressure and is often practically or even technically not feasible.

In practice, therefore, the standards ISO 3382-1 and ISO 3382-2 specify to measure the time taken for the reverberation to decay by 20 dB or 30 dB only. These readings can then be linearly extrapolated to a decay time of 60 dB.

• T20 = 3 * (time to decay by 20 dB) while
• T30 = 2 * (time to decay by 30 dB)

Generally, it is better to choose T30 over T20, as the measurement uncertainty will be lower. However, if the background noise is too high and/or the sound source is not loud enough to create an extra 45 dB, T20 may be your best option.

A single Reverberation Time result may be calculated by averaging measured values from a selection of frequency bands. For example, a single figure reverberation time may be calculated by averaging the results of the 500 Hz and 1000 Hz octave bands.

(0.67 + 0.59) / 2 = 0.63

This result may be represented thus: T_{[500Hz, 1000Hz]} = 0.63 seconds

Alternatively, for third-octave measurements, you may take averages over the six bands from 400 Hz to 1250 Hz.

(0.34 + 0.36 + 0.25 + 0.22 + 0.23 + 0.22) / 6 = 0.27

This result may be represented thus: T_{[400Hz-1.25kHz]} = 0.27 seconds

According to the ISO 3382-1 standard, either of the above two results may be labelled T_mid.

The process and the XL2 Acoustic Analyzer are designed to be operated by one person.

However, although it is loud and therefore possibly uncomfortable, there can be other people in the room during the measurement. It may, for example, be useful for you to have help moving the dodecahedron around.

Everyone in the room must remain still and quiet during measurements. They should all wear hearing protection. Avoid anyone standing near the microphone.

People who are present in the room during the measurement will absorb sound energy and possibly reduce the reverberation time value. You should document how many people were present during measurements.