Energy Relationships In Sound

The magnitudes most used to describe the energy involved in sound or noise are sound pressure and sound power. Pressure, either static (barometric) or dynamic (sound vibrations), is the magnitude most easily observed. Sound pressure is usually measured as an RMS value—whether this value is specified or not—but peak values are sometimes also used.

From the threshold of hearing to the threshold of pain, sound pressure values range from 0.0002 to 1000 or more dynes per square centimeter (Table 6.1.1). To permit this wide range to be described with equal resolution at all pressures, a logarithmic scale is used, with the decibel (dB) as its unit. Sound pressure level (SPL) is thus defined by where P is measured pressure, and Pref is a reference pressure. In acoustic work this reference pressure is 0.0002 dynes/cm2. (Sometimes given as 0.0002 microbars, or 20 micronewtons/meter2. A reference level of 1 microbar is sometimes used in transducer calibration; it should not be used for sound pressure level.) Table 6.1.2 lists a few representative sound pressures and the decibel values of sound pressure levels which describe them.

This logarithmic scale permits a range of pressures to be described without using large numbers; it also represents the nonlinear behavior of the ear more convincingly. A minor inconvenience is that logarithmic quantities cannot be added directly; they must be combined on an energy basis. While this combining can be done by a mathematical method, a table or chart is more convenient to use; the accuracy provided by these devices is usually adequate.

Table 6.1.3 is suitable for the purpose; the procedure is to subtract the smaller from the larger decibel value, find the amount to be added in the table, and add this amount to the larger decibel value. For example, if a 76 dB value is to be added to an 80 dB value, the result is 81.5 dB (80 plus 1.5 from the table). If more than two values are to be added, the process is simply continued. If the smaller of the two values is 10 dB less than the larger, it adds less than 0.5 dB; such a small amount is usually ignored, but if several small sources exist, their combined effect should be considered.

The sound power of a source is important; the magnitude of the noise problem depends on the sound power. Sound power at a point (sound intensity) cannot be measured directly; it must be done with a series of sound pressure measurements.

The acoustic power of a source is described in watts. The range of magnitudes covers nearly 20 decimal places; again a logarithmic scale is used. The reference power level normally used is 10—12 watt, and the sound power level (PWL) is defined by

or, since the power ration 10—12 means the same as —120 dB, the following equation is also correct:

6.1(6) In either case, W is the acoustic power in watts.

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