7.1 Combining sounds across time (total sound exposure)

The same principle can be used if we need to add up sound levels across time. For example in noise exposure calculations we often have several different exposure levels received for different durations during a day, and we need to calculate the average noise exposure over an 8hr day.

The general principle is the same, we need to work out the intensity for each exposure but we also need to multiply each exposure by its duration before adding them all together and then dividing by the total time to get an average exposure which is then converted back to decibels (usually dB(A) for noise exposure calculations).

So, for example if we have exposures measured as L₁dB(A), L₂dB(A), L₃dB(A), ... L_ndB(A) for durations t₁, t₂, t₃, ... t_n respectively and a total time over which the average is to be taken of T then an average can be calculated. This average is usually referred to as the equivalent continuous noise level (L_eq) and is given by:

(7.1)

While this equation may look complex, you can see that each bit within the brackets is simply each sound level converted from a dB scale and then multiplied by its duration before taking the average.

If we are concerned with the daily exposure of a particular person then T is taken as 8 hours in the above equation and the equation becomes that for the personal daily exposure level (L_EP,d). Note, it is entirely possible for the individual exposure durations to add up to more than an 8 hour day (i.e. t1 + t2 + t3 + ... +tn > 8hrs)This situation would simply mean that the person is working more than an 8hr day, but we still make the calculations over 8hrs. So equation (5.5) becomes:

   (7.2)