# 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.

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 93 85 12 150 91.76 85 8 100 90 85 4 50 87 85 2 25 84 85 1 12.5 81

### 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

### Threshold

There is another element to % Dose, which is the cut-off 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 anti-log
• D = Percentage exposure (%)
• TC = Criterion sound duration (usually 8hours)
• T = Measurement duration in hours
• L = Weighted sound level
• LC = Criterion sound level (usually dB(A)
• q = (Exchange rate parameter(dB)).
• =10 for an exchange rate of 3dB
• = 5/log10 (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 ith time interval.
• ti= Time spent in the ith 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.
• LC = Typically 90dBA in the UK sometimes 85dBA in other countries.
• D = indicated dose index (%).
• TC = reference time base 8 hours.
• TM = measurement time in hours.

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