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# Sound - Leq - Equivalent Level

## The EPA Equivalent Sound Level - Leq - quantifies the noise environment to a single value of sound level for any desired duration.

The Environmental Protection Agency - EPA - has adopted a system of four "sound descriptors"

to summarize how sound is heard and measured, and to determine the impact of noise on health and welfare.

### Equivalent Sound Level - Leq

Equivalent Sound Level - Leq - quantifies the noise environment to a single value of sound level for any desired duration. It is designed to represent a varying sound source over a given time as a single number. Leq is also sometimes known as Average Sound Level - LAT even if this is not.

This descriptor correlates well with the effects of noise on people.

Equivalent Sound Level - Leq - can be calculated by integrating the sound pressure level over a time period as:

Leq = 10 log [(1/T) ∫ (pA / pref)2 dt ]                               (1)

where

Leq = equivalent sound level (dB)

T = time period (s)

pAsound pressure (Pa, N/m2)

pref = reference sound pressure ( 2 10-5  Pa, N/m2)

Equivalent sound levels can be added together as

Leg_total = 10 log (1 / (t1  + t2 ... tn) (t1 10Leq_1/10 + t2 10Leq_2/10 + ... + tn 10Leq_n/10))                    (2)

where

Leg_total = total equivalent sound level (dB)

#### Example - Equivalent Sound Level

A machine generates a sound pressure of 0.02 Pa half the time when idling and 0.1 Pa the other half of the time when working.

The equivalent sound level for half an hour idling can be calculated as

Leq_idling = 10 log [(1/(0.5 hour)) ((0.02 Pa)/(2 10-5 Pa))2 (0.5 hour)]

= 60 dB

The equivalent sound level for half an hour working can be calculated as

Leq_working = 10 log [(1/(0.5 hour)) ((0.1 Pa)/(2 10-5 Pa))2 (0.5 hour)]

= 74 dB

The equivalent sound level for one hour running can be calculated as

Leq_running = 10 log [ (1 / ((0.5 hour) + (0.5 hour))) (  ((0.02 Pa) / (2 10-5 Pa))2 (0.5 hour) + ((0.1 Pa) / (2 10-5 Pa))2 (0.5 hour) ) ]

= 71.2 dB

The equivalent sound level for one hour running can alternatively be calculated with (2) as

Leg_total = 10 log ((1 / ((0.5 hour) + (0.5 hour)) ((0.5 hour) 10(60 dB)/10 + (0.5 hour) 10(74 dB)/10))

= 71.2 dB

### Equivalent Sound Level Calculator

Use the calculator below to calculate equivalent sound level:

Leq_1 - equivalent sound level 1 (dB)

time 1 (h, min, s)

Leq_2 - equivalent sound level 2 (dB)

time 2 (h, min, s)

## 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.

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