Sound - L_eq - Equivalent Level

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

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_eq is also sometimes known as Average Sound Level - L_AT even if this is not.

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/m²)

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

Equivalent sound levels can be added together as

L_{eg_total} = 10 log (1 / (t₁  + t₂ ... t_n) (t₁ 10^L_{eq_1}/10 + t₂ 10^L_{eq_2}/10 + ... + t_n 10^L_{eq_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)

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