All so confusing: the decibel

28th January 2022 By: Terry Mackenzie-hoy

Okay, here are your questions. Take your time; answer ‘yes’ or ‘no’. (a) Are decibels used to measure sound power? (b) Are decibels used to measure sound pressure level? (c) Are decibels used to measure sound intensity? (d) Are decibels used to measure electrical signal levels?

The answer to all these questions is ‘yes’. The sound given off by a source has a power in watts and, at a distance from the source, we hear sound as sound intensity in watts per square metre. The human ear can hear a pin drop and also hear the sound of a fighter jet taking off. Expressed as a formula, the intensity of a sound in decibels is 10 log10 (S1/S2), where S1 and S2 are the intensity of the two sounds. The range of hearing is vast: from 0.000000000001 W/m2 to 0.01 W/m2. This is a range of 10-billion. Quite obviously, using decibels to express these quantities is much more convenient. What is done is to divide the sound measured by the threshold of hearing (0.0000000000001 W/m2), take the logarithm and multiply by 10. Thus, if the sound intensity of an electric drill is 0.00001 W/m2, then the sound intensity in decibels is 70 dB. No problem, huh? Well, you may be wondering what a logarithm is. It is a number expressed as a power of 10. For example, 100 = 102 so the logarithm of 100 is 2, 10 000 = 104 so the logarithm of 10 000 is 4. It happens that all numbers can be expressed as logarithms to base 10. The simplest way to do this is to enter the number in your calculator, press the ‘log’ key and there you go. But wait, there’s more –

unfortunately, it is very difficult to measure sound intensity. But sound pressure is proportional to the square of intensity so, if you have a suitably adjusted instrument and measure sound pressure levels, you will be measuring sound intensity, which is what humans hear. But wait, there’s more –

humans don’t hear all sounds the same. We don’t hear low frequencies (drones and rumbles) very well and we generally don’t hear high frequencies (whines and whistles) beyond about 8 kHz. Thus, sound-level meters are designed with filters which adjust the level of certain frequencies down and certain frequencies up to mimic human hearing. Sound pressure levels measured in this way are expressed as a sum of all levels across a number of frequency bands. This is called A-weighting and decibels thus measured are known as ‘decibels A-weighted’, or dBA.

Just about every single journalist or member of the public gets this wrong: they refer to the magnitude of sound as being in decibels (without a given frequency) when they should use ‘decibels A-weighted’. But wait, there’s more – sound under water is not the same as sound in air. In air, sound travels at about 340 m/s. In water, it is about 1 450 m/s. For this reason and other factors (salinity, pressure, temperature) decibels under water are not the same. Decibels under water are relative to a value of one picowatt, while in air they are relative to 20 micropascal. In a gross generalisation, to convert from water to air, simply subtract the 62 dB from the sound level in water. Thus, when a very senior journalist wrote that the seismic array gun sound was “10 000 times louder than a nuclear explosion”, I wrote to correct him and pointed out: “I read about the noise levels from Shell’s seismic ships being louder than a nuclear explosion. This is not the case – sound pressure levels in water are not the same as in air.” He ignored me.

But anyway, it matters not. It is, however, as far as I know, there is no undergraduate course in acoustics available at any South African university (if I am wrong, do let me know). The result of this is that practising acoustics engineers are getting older and fewer, and ignorance of the subject grows and grows. Pity.