The Physics, Physiology, and Psychology of Noise

by Dr. Jeremy Tatum, University of Victoria
This is the essence of a talk delivered by Dr. Tatum to the annual general meeting of the SSAP in November 1996.

The intensity of sound is measured in units called decibels and is measured with an instrument called a decibel meter. But have you ever had this experience? You complain to your local council that you are being annoyed by a noise made by a source that you identify and which is trespassing into your property. Council sends round an Official armed with a Decibel Meter who then takes Measurements. What, you wonder, can possibly be the purpose of these measurements? Does not the council already have all the relevant information? You have told them that there is a noise, and where the noise is coming from, that it is trespassing on your property and that it is annoying you. What more information is required? Is the Official taking measurements to verify that you are in fact annoyed? Could you perhaps be mistaken and the noise does not annoy you after all? Or, if you really are annoyed, is the Official perhaps taking measurements to see how annoyed you are?

In this talk I shall try to distinguish between the physics, the physiology and the psychology of noise. I shall point out that some municipal bylaws make it an offence to exceed a certain decibel level, while others make it an offence to annoy you. While the first type of bylaw may seem to be more "objective" and therefore workable, I shall argue that in practice it is unenforceable and that the degree of annoyance of a noise is not closely related to the decibel level, and that the bylaw you should favour is one that makes it an offence to annoy you.


Sound is a form of energy, and in physics, energy is expressed in units called joules. Rate of production of energy, or power, is expressed in watts, a watt being one joule per second.

As far as I am concerned, a machine may generate as many watts of acoustic power as it likes as long as it is a hundred miles from me and I can't hear it. What concerns me as a sufferer from noise is flux (Latin = flow) of acoustic energy arriving at my location. This is the rate of flow of acoustic energy arriving at my location in watts per square metre. A sound of a million watts is of no concern if it is spread out over a square kilometre; but if it is concentrated in a square centimetre in the vicinity of my eardrum I am very concerned indeed.

Now a scientist would be quite content to express acoustic energy flux in watts per square metre and have done with it; but, for no particularly good reason, engineers prefer to use a decibel (dB) scale. The decibel level is merely another way of expressing acoustic energy flux, and, for those who are interested in and understand such things, the relation between the flux F in watts per square metre and the decibel level D is

           D = 10 log F + 120.
What this means is that, for every increase of 10 dB, there is a tenfold increase in the energy flux. Thus

What can those of you who are neither scientists nor engineers rescue from this that is understandable in terms of the cacophony that you have to put up with?

Sixty decibels is sometimes described as being about the level of conversation. Well, we all know people who do talk that loud. I would describe 60 dB as more like shouting; 55 dB is more like civilized discourse. But, just be aware that the Official who took Measurements in response to your complaint is likely to report back to the Authorities that the noise level is "only" 58 dB, which has been set in some parts of Saanich [British Columbia], for example, as perfectly legal and is less than the level of conversation; and consequently the Official has determined that you were quite mistaken in your belief that the noise was annoying you. Let me put it this way, however. If there was a noise in this room at 58 dB, you would not be able to hear what I am saying. Whenever you are asked to say what is meant by a noise level of 58 dB, you should not say that it is about the level of conversation; rather, it is the level of noise that seriously interferes with normal conversation.


Well, it has been nice and easy so far. We have been doing physics, a nice and simple subject. It is now time to move on to something more difficult -- physiology. What we have to deal with here is not merely the energy flux is watts per square metre, but the perceived loudness. The ear is not equally sensitive to all frequencies, nor even at one frequency is its response directly proportional to the energy flux or even to its logarithm. It varies from individual to individual, and with age for a given individual.

If you were to look at a chart showing the sensitivity of the human ear to different intensities and frequencies, there is one thing you would all agree upon -- it is very complicated! Hidden in such a chart is the common misconception that an increase of ten decibels corresponds to a increase in perceived loudness of a factor of only two. In practice a subject cannot in general say when he or she perceives one sound as being twice as loud as another.

What is done in studying perceived loudness is to ask a subject to listen to two sounds of different frequencies and intensities, and for the subject to say when the two sounds are of equal perceived loudness. I shall spare you the details, but I'll just mention that for pure tones perceived loudness is expressed in units called sones or phons. A sone is analogous to the acoustic energy flux in watts per square meter, and a phon is analogous to its logarithmic counterpart in decibels. The zero point of the phon scale is set so that for a pure tone at 1000 Hz (Hz is short for hertz, one hertz being a frequency of one cycle per second) the phon and decibel levels are equal. The relationship between phons (P) and sones (S) is approximately

         P = 33.22 log S + 40
and those to whom this equation means something will be able to verify that a doubling of the number of sones corresponds to an increase of 10 phons.

For sounds that are not pure tones but which cover a wide frequency range, which is the usual situation, there are analogous units. The noy (which suggests both noise and annoyance) is analogous to sones or to watts per square metre; and its logarithmic counterpart, PNdB, which is short for perceived noise in decibels, is analogous to the decibel scale. A similar equation holds:

        PNdB = 33.22 log N + 40.
Here N is the number of noys, and again the mathematically inclined will recognize that doubling the number of noys results in an increase of 10 in the PNdB.
But none of this -- not the physics, which measures the energy flux in watts per square metre, nor the physiology, which attempts to quantify with sones and phons the average response of the human ear -- tells us very much if anything at all about how annoying an intrusive noise can be. We have to enter the even more difficult realm of


Is it possible to express quantitatively how disturbing a noise is to those who have it inflicted upon them? Attempts have been made to measure annoyance quantitatively by recording the number of complaints received. But this fails because people cease to complain when their complaints are not treated seriously or are treated with hostility.

I want to give three examples to illustrate that the decibel levels or the phon levels or the PNdB are by no means the only or even the most important factors in noise disturbance. They may even be scarcely relevant. My examples consist of three pairs of sounds, in one of which the acoustic energy flux is twice as much as in the other -- a difference of 3 decibels. Ask yourself which is the more annoying sound: the 58 dB sound, or the "quieter" 55 dB sound.

1. (a) 58 dB for 5 seconds?
   (b) 55 dB for 5 hours?

2. (a) 58 dB at 3:00 p.m.?
   (b) 55 dB at 3:00 a.m.?

3. (a) a Mozart piano sonata at 58 dB?
   (b) someone scraping fingernails on a blackboard at 55 dB?
These examples illustrate that none of the complicated mathematical equations relating phons to sones or noys or decibels, and none of the Important Measurements made by our Official, even begin to address how annoying a noise can be. Indeed, the decibel level hardly seems to be relevant at all.

This conclusion is of crucial practical importance, for the following reason. There are two types of municipal bylaw, which read something like this:

"No person shall make or cause or permit to be made or caused any noise that disturbs or tends to disturb the quiet, peace, rest, enjoyment, comfort or convenience of persons..."
"No person shall make, cause or permit to be made a sound that exceeds, at a point of reception, 58 decibels..."

The latter type is often held to be "better" in that it is "more objective." I strongly argue against this. In the first place, the decibel level is usually set far too high -- our specimen sets a level that will seriously interfere with normal conversation. And once that bylaw is passed, you are stuck with it: it is now perfectly legal for someone to interfere with your conversation.

But more seriously, such a bylaw is unenforceable, and may well be designed to be. Most of the noise that disturbs you does so in the evenings, at weekends and at night-time, or it may be transitory -- a truck, for example, with its motor running or hooter sounding for twenty minutes. The Official with his Decibel Meter is unavailable at the hours when you are being most disturbed by the noise, and, even if it is during working hours, the offending truck will be long gone by the time the Official arrives (which will probably be several weeks later, if at all).

My conclusion is this: a person is a nuisance not by making a noise above a certain decibel level (which may not actually be annoying anybody) but by causing a disturbance to his or her neighbours, and that is the criterion that should be tested in the bylaws to determine if there is an offence. Residents in my apartment, for example, twice took cases to court when our bylaw was of the "annoyance" type -- and we won. As a consequence, the municipality changed the bylaw to a "decibel" type in order to prevent any further complaints from us -- and we have had no recourse against unwanted or unwonted noise ever since.

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