In a sound wave there are extremely small periodic variations in atmospheric pressure to which our ears respond in a rather complex manner. The minimum pressure fluctuation to which the ear can respond is less than one billionth (10-9) of atmospheric pressure. (This is even more remarkable when we consider that storm fronts can cause the atmospheric pressure to change by as much as 5 to 10% in a few minutes.) The threshold of audibility, which varies from person to person, typically corresponds to a sound pressure amplitude of about 2x10-5N/m2 at a frequency of 1000 Hz. The threshold of pain corresponds to a pressure amplitude approximately one million (106) times greater, but still less than 1/1000 of atmospheric pressure.
Because of the wide range of pressure stimuli, it is convenient to measure sound pressures on a logarithmic scale, called the decibel (dB) scale. Although a decibel scale is actually a means for comparing two sounds, we can define a decibel scale of sound level by comparing sounds with a reference sound having a pressure amplitude Po = 2 X 10-5N/m2 assigned a sound pressure level of 0 dB. Thus we define sound pressure level as:
Lp = 20 log P/Po.
Expressed in other units, Po =20 JLPa = 2 x 10-4dynes/cm2 = 2 X 10-4 microbars. (For comparison, atmospheric pressure is 105 N/m2, or 106 microbars). Sound pressure levels are measured by a sound level meter, consisting of a microphone, an amplifier, and a meter that reads in decibels.
In addition to the sound pressure level, there are other levels expressed in decibels, so one must be careful when reading technical articles about sound or regulations on environmental noise. One such level is the sound power level, which identifies the total sound power emitted by a source in all directions. Sound power, like electrical power, is measured in watts (one watt equals one joule of energy per second). In the case of sound, the amount of power is very small, so the reference selected for comparison is the picowatt (10-12 watt). The sound power level (in decibels) is defined as
Lw = 10 log W /Wo,
where W is the sound power emitted by the source, and the reference power Wo = 10-12 watt.
Another quality described by a decibel level is sound intensity, which is the rate of energy flow across a unit area. The reference for measuring sound intensity level is 10 = 10-12 watt/m2, and the sound intensity level is defined as
L1 = 10 log 1/10,
For a free progressive wave in air (e.g., a plane wave traveling down a tube or a spherical wave traveling outward from a source), sound pressure level and sound intensity level are nearly equal (Lp ~ L1) This is not true in general, however, because sound waves from many directions contribute to sound pressure at a point.
The relationship between sound pressure level and sound power level depends on several factors, including the geometry of the source and the room. If the sound power level of a source is increased by 10 dB, the sound pressure level also increases by 10 dB, provided everything else remains the same. If a source radiates sound equally in all directions and there are no reflecting surfaces nearby (a free field), the sound pressure level decreases by 6 dB each time the distance from the source doubles.
Loudness is a subjective quality. While loudness depends very much on the sound pressure level, it also depends upon such things as the frequency, the spectrum, the duration, and the amplitude envelope of the sound, plus the environmental conditions under which it is heard and the auditory condition of the listener.
Loudness is frequently expressed in sones. One sone is equal to the loudness of a 1000-Hz tone at a 40-dB sound pressure level, and two sones describes a sound that is judged twice as loud, etc. The dependence of subjective loudness on sound pressure is discussed in connection with Demonstration 7.