Acoustics and Psychoacoustics: Introduction to sound - Part 2

SWL = 10 log₁₀ (w_actual/w_ref)                                         (1.11)

where w_actual = the actual sound power level (in watts)
and w_ref = the reference sound power level (10^-12 W)

The sound power level is useful for comparing the total acoustic power radiated by objects, for example ones which generate unwanted noises. It has the advantage of not depending on the acoustic context, as we shall see in Chapter 6. Note that, unlike the sound intensity, the sound power has no particular direction.

1.2.3 Sound pressure level
The sound intensity is one way of measuring and describing the amplitude of a sound wave at a particular point. However, although it is useful theoretically, and can be measured, it is not the usual quantity used when describing the amplitude of a sound. Other measures could be either the amplitude of the pressure, or the associated velocity component of the sound wave.

Because human ears are sensitive to pressure, which will be described in Chapter 2, and because it is easier to measure, pressure is used as a measure of the amplitude of the sound wave. This gives a quantity which is known as the sound pressure, which is the root mean square (rms) pressure of a sound wave at a particular point. The sound pressure for real sound sources can vary from less than 20 micropascals (20 µPa or 20 - 10^-6 Pa) to greater than 20 pascals (20 Pa).²

Note that 1 Pa equals a pressure of 1 newton per square metre (1 N m^-2). These two pressures broadly correspond to the threshold of hearing (20 µPa) and the threshold of pain (20 Pa) for a human being, at a frequency of 1 kHz, respectively. Thus real sounds can vary over a range of pressure amplitudes which is greater than a million to one. Because of this, and because of the way we perceive sound, the sound pressure level is also usually expressed on a logarithmic scale. This scale is based on the ratio of the actual sound pressure to the notional threshold of hearing at 1 kHz of 20 µPa. Thus the sound pressure level (SPL) is defined as:

SPL = 20 log₁₀(p_actual/p_ref)                                         (1.12)

where p_actual = the actual pressure level (in Pa)
and p_ref = the reference pressure level (20 µPa)

The multiplier of 20 has a twofold purpose. The first is to make the result a number in which an integer change is approximately equal to the smallest change that can be perceived by the human ear. The second is to provide some equivalence to intensity measures of sound level as follows.