# L_{eq} - Equivalent Sound Level

## Equivalent Sound Level - L_{eq} - 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"

- A-weighted sound level
- Sound Exposure Level -
*L*_{s} - Equivalent Sound Level -
*L*_{eq} - Day-Night Sound Level -
*L*_{dn}

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

### Equivalent Sound Level - *L*_{eq}

_{eq}

Equivalent Sound Level - *L _{eq}* - 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.

*L*is also sometimes known as Average Sound Level

_{eq}*- L*even if this is not.

_{AT}This descriptor correlates well with the effects of noise on people.

Equivalent Sound Level - *L _{eq}* - can be calculated by integrating the sound pressure level over a time period as:

L_{eq}= 10 log [(1/T) ∫ (p_{A}/ p_{ref})^{2}dt ] (1)

where

L_{eq}= equivalent sound level (dB)

T = time period (s)

p_{A}= sound pressure (Pa, N/m^{2})

p_{ref}= reference sound pressure ( 2 10^{-5}Pa, N/m^{2})

Equivalent sound levels can be added together as

*L _{eg_total} = 10 log (1 / (t_{1} + t_{2} ... t_{n}) (t_{1} 10^{Leq_1/10} + t_{2} 10^{Leq_2/10} + ... + t_{n} 10^{Leq_n/10})) (2)*

*where *

*L _{eg_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

*L _{eq_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

*L _{eq_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

*L _{eq_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

*L _{eg_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:

*L _{eq_1} - equivalent sound level 1 (dB)*

* time 1 (h, min, s)*

* L _{eq_2} - equivalent sound level 2 (dB)*

* time 2 (h, min, s)*