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Sound and the Decibel

Sound can be defined as any pressure variation that propagates through the air, or any other 'medium' for that matter, that can be detected by the human ear. The weakest sound pressure that can be detected by a healthy ear is 20 micropascals. Remarkably, the human ear can tolerate sound pressures more than one million times higher than this.

Therefore, if sound level were measured in terms of pascals, you would end up with some impractically large numbers. To circumvent this problem, sound levels can be specified using a decibel or ‘dB’ scale. Decibels are defined as 10 times the logarithm of the ratio of two quantities that are measured in terms of power W as follows:

Note that the word ‘level’ is always included when dealing with decibels. Now, because acoustic power is proportional to the square of the pressure, the equation above can be rewritten as:

Using the decibel scale in this way compresses the impractically large range of pressure values into a much more manageable size. If a reference pressure (Po) of 20 micropascals is used, then the range of human hearing extends from 0dB all the way up to about 120dB, which is when sound starts to become intolerable. However, when a sound at any level becomes unpleasant, unwanted or annoying it is usually referred to as noise.

Conveniently, the decibel scale also provides a much better approximation to how we perceive ‘loudness’ than the pascal scale. For example, a change in SPL from 40dB to 45dB results in roughly the same change in apparent loudness as when going from 45dB to 50dB, and so on. For most people, a 3dB change in SPL up or down is the smallest change that is detectable, and a 6dB change, equivalent to a doubling or halving of the sound pressure, is clearly perceptible. Studies have shown that to make a sound seem roughly twice or half as loud requires a 10dB change in SPL.

When two or more sound sources are brought together or combined, the overall level cannot be calculated by simply adding up their individual decibel values. This is because sound sources add together on a logarithmic basis. If two identical noise sources are placed together, their combined noise level is 3dB higher than the individual levels, which is equivalent to a doubling of sound energy. If a difference of 10dB or more exists between two sources, then the combined level is practically the same as the higher of the two individual levels.

Sound pressure levels can be easily measured with a sound level meter. The measured SPL depends on how far away the meter is from the noise source, and on the local measuring environment. For noise that fluctuates in level, an ‘integrating’ sound level meter is used to calculate the Equivalent Continuous Level, or Leq for short. The Leq is basically the average SPL measured over a given period of time.

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