Appendix A - Sound Pressure Level Calculations
Sound pressure level in decibels is defined in the following way:
dB = 20 log (Sound Pressure/Reference Pressure)
The "log" or logarithm of a number is a mathematical manipulation of the number, based on multiples of 10. It is the exponent that indicates the power to which the number 10 is raised to produce a given number. For example, the logarithm of 10 is 1 since 10 is multiplied by itself only once to get 10. Similarly, the logarithm of 100 is 2 since 10 times 10 is 100. The logarithm of 1000 is 3 since 10 times 10 times 10 is 1000.
Therefore
log(1) = 0 Since 10 to the exponent 0 = 1,
log(10) = 1 since 10 to the exponent 1 = 10,
log(100) = 2 since 10 to the exponent 2 = 100,
log(1000) = 3 since 10 to the exponent 3 = 1000
The logarithm scale simply compresses the large span of numbers into a manageable range. In other words, the scale from 10 to 1000 is compressed, by using the logarithms, to a scale of 1 to 3.
The decibel scale for sound pressures uses as the reference pressure the lowest noise that the healthy young person can hear (0.00002 Pa). It divides all other sound pressures by this amount when calculating the decibel value. Sound pressures converted to the decibel scale are called sound pressure levels, abbreviated Lp. So, the sound pressure level of the quietest noise the healthy young person can hear is calculated in this way:
Lp = 20 log ( 0.00002/ 0.00002) = 20 log (1) = 20 X 0 = 0 dB
The sound pressure level or Lp in a very quiet room, where the sound pressure is 0.002 Pa, is calculated:
Lp = 20 log (0.002/ 0.00002) = 20 log (100) = 20 X 2 = 40 dB
The sound pressure level of a typical gasoline-powered lawn mower, which has a sound pressure of 1 Pa, is calculated
Lp = 20 log (1/0.00002) = 20 log (50 000) = 20 X 4.7 = 94 dB
