Noise – What is Dose and how is it calculated?
In acoustics, what is noise Dose, how is it calculated and what is it used for?
Dose is a measure of noise exposure and is directly related to Lex, in the UK Dose is also described as the HSE ‘Points’ system.
It is best described with the following statement:
100% Dose (or 100 points) = 85dBA for 8 hours. This is known as the ‘Criterion’ level
In other countries, Dose may be specified with a different criterion i.e. 100% Dose = 90dBA for 8 hours may also be specified.
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The tables below give examples of how DOSE is related to exposure time and Lex (Lep’d) (assuming 100% Dose = 85dBA for 8 hours.)
Effect of changing SPL
Lp (dBA)  Exposure Time (hours)  Dose (%)  Lex/Lep’d (dBA) 
94  8  800  94 
91  8  400  91 
88  8  200  88 
85  8  100  85 
82  8  50  82 
79  8  25  79 
Effect of changing Exposure Time
Lp (dBA)  Exposure Time (hours)  Dose (%)  Lex/Lep’d (dBA) 
85  16  200  88.01 
85  12  150  86.76 
85  8  100  85 
85  4  50  81.99 
85  2  25  78.98 
85  1  12.5  75.97 
Effect of changing SPL and Exposure Time
Lp (dBA)  Exposure Time (hours)  Dose (%)  Lex/Lep’d (dBA) 
88  4  100  85 
85  8  100  85 
80  8  31.6  80 
82  4  25  79 
79  4  12.5  76 
Exchange Rate
Each time the sound level increases by 3dB, the Dose doubles given the same exposure time. Similarly, if the sound level decreases by 3dB, the Dose will halve for the same exposure time. This number is called the exchange rate.
Doubling the exposure time doubles the Dose, and halving the exposure time halves the Dose given the same sound level.
In some countries, the exchange rate is changed to 4,5 or sometimes even 6. This means that the percentage level will change more slowly in respect of a changing sound exposure level.
The following tables show the relationship between the exchange rate, the criterion level and the noise exposure limits
The effect of different Exchange Rate and Criterion
Noise Exposure Limits (Criterion Level = 80dB)  
Max Permitted Daily Duration (Hours)  3dB Exch Rate Allowable Level (dB)  4dB Exch Rate Allowable Level (dB)  5dB Exch Rate Allowable Level (dB) 
8  80  80  80 
4  83  84  85 
2  86  88  90 
1  89  92  95 
0.5  92  96  100 
0.25  95  100  105 
Noise Exposure Limits (Criterion Level = 85dB)  
Max Permitted Daily Duration (Hours)  3dB Exch Rate Allowable Level (dB)  4dB Exch Rate Allowable Level (dB)  5dB Exch Rate Allowable Level (dB) 
8  85  85  85 
4  88  89  90 
2  91  93  95 
1  94  97  100 
0.5  97  101  105 
0.25  100  105  110 
Relationship between %Dose and Time with an Leq of 85dBA
Relationship between Leq and Lep’d (Lex)
Threshold
There is another element to % Dose, which is the cutoff point at which the dose is accumulated. This would normally be set to 0, 5 or 10 and means the level below the 100% point where sound is counted towards the total %Dose. If the threshold is set to 10 and the criterion (100% level) is 85dB, the any sound below 75dB will not be added to the percentage dose figure.
How Dose works mathematically
The operation of Dose can be the mathematically described by the equation below, which relates the percentage exposure D to the integrated sound power.
Mathematical description of %Dose:
Where:
 ↑ represents the antilog
 D = Percentage exposure (%)
 T_{C }= Criterion sound duration (usually 8hours)
 T = Measurement duration in hours
 L = Weighted sound level
 L_{C} = Criterion sound level (usually dB(A)
 q = (Exchange rate parameter(dB)).
 =10 for an exchange rate of 3dB
 = 5/log_{10} (2) for an exchange rate of 5dB.
With respect to Lc, criterion levels of 90 and 85 dB(A) are most often used.
For discrete time intervals at a constant sound level, the equation above, “Mathematical description of %Dose”, can be rewritten as:
Where:
 Li= Weighted sound pressure level in the i^{th} time interval.
 ti= Time spent in the i^{th} interval in hours.
Example:
Calculate the daily (8 hr) noise exposure of a machine operator where the noise levels are constant at i)90 dB(A) and ii)100 dB(A). Use an exchange rate of 3dB and a criterion level of 90 dB(A).
Since the sound level is constant throughout the day, i.e. 90 dB(A) Equation 14: Dose Calculation from discreet time intervals, reduces to:
 ti = 8 hr, Tc =8 hr, Li = 90 dB(A), Lc = 90 dB(A), q =10.
 L=100 dB(A).
The Dose can be converted to an Leq by the following formula.
Where:
 Leq = the equivalent continuous sound level, with A weighting, from the time TM.
 L_{C} = Typically 90dBA in the UK sometimes 85dBA in other countries.
 D = indicated dose index (%).
 T_{C} = reference time base 8 hours.
 T_{M} = measurement time in hours.
Here are some Sound Meters which measure in Noise Dose:
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