Sound
intensity I is defined as the ratio of the power output of a sound source
and the area over which the sound energy is distributed. The unit of intensity is
Watts per square meter (w/m2).
Sound
intensity I is defined as the ratio of the power output of a sound source
and the area over which the sound energy is distributed. The unit of intensity is
Watts per square meter (w/m2).
Sound energy travels outward from a point source on spherical wavefronts. The speed is constant (~330 m/s). The energy spreads out over larger and larger area. The area is the surface of a sphere: A=4pr2, where r is the radial distance from the source. Thus,
which means that at double the distance from the point source, the sound intensity drops to one fourth of what it was originally.
The range of intensities for human hearing is very wide:
Imax = 1.0 w/m2 for sound intense enough to damage hearing.
So physicists invented a logarithmic scale for loudness b, based on powers of ten:
which has the unit decibel (dB). b = zero dB for a barely-audible sound (at the threshhold for hearing), and b = 120 dB for the loudest tolerable sound.
Sound production and amplification equipment (a recording device connected to a microphone, for example) has meters or digital readouts with negative decibels in some cases. Obviously, sound intensities too low to be heard can be produced or detected. Also, the decibel scale may simply be used as a measure of the ratio between two signal strengths (one of them a reference "intensity").