Sound  L_{eq}  Equivalent Level
The EPA 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"
 Aweighted sound level
 Sound Exposure Level  L_{s}
 Equivalent Sound Level  L_{eq}
 DayNight 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/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)
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.
Related Documents

Decibel A, B and C
Sound pressure filters that compensates for the hearing sensed by the human ear. 
NC  the Noise Criterion
Noise Criterion  NC  level is a standard uesd to describe the relative loudness of a space within a range of frequencies. 
Noise  Acceptable dB_{A} Level
Acceptable noise  dB_{A}  level at typical common locations. 
Noise  EPA Protective Levels
The noise level should not exceed certain values to protect public health and welfare. 
Noise  Recommended Exposure Limits (REL)
The NIOSH noise Recommended Exposure Limit  REL  for occupational noise 
Sound  L_{dn}  Day and Night Level
The EPA Aweighted sound level day and night equivalent definition  L_{dn}  for a 24 hour period. 
Sound  L_{s}  Exposure Level
The EPA Sound Exposure Level  L_{s}  describes the noise from a variable source. 
Sound Pressure Level  OSHA AWeighted per Day
OSHA maximum Aweighted sound pressure levels allowed per day.