11.1. Transmission of Sound http://www.ck12.org
beat frequency isfb= 268 Hz− 261 Hz= 7 Hz. Of course, a beat frequency exists in principle between any two
frequencies, but the human ear has difficulty hearing the “beat” beyond several hertz. Instead, we hear the two
frequencies separately.
http://demonstrations.wolfram.com/BeatsWorking/
Sound Intensity
Theintensityof a wave is defined as the average power produced by some source (a horn and a light bulb are two
examples) divided by the surface area over which the energy is transmitted. The equation for the intensity is:I=WA
Irepresents intensity,Wpower (the wattage), andAthe area over which the energy, in a given amount of time, has
spread.
IntensityIhas units of watts per square meter. Recall that a watt is joule per second, orJS.
Since power is a measure of energy per unit time, the intensity depends upon the rate at which the energy is produced.
The intensity is dependent upon the frequency of vibration of the source, as well as the density of the medium.
Perhaps the most obvious factor determining the intensity, though, is the amplitude of the source.
We stated earlier that the amplitude of a sound is associated with the loudness of that sound. Strike a tuning fork
gently and the displacement (the amplitude) of the prongs is small and the sound is soft. Strike the tuning fork
harder and the amplitude of the prongs is larger and the sound is increased. We state without proof, for spherical
waves, if only the amplitude of a wave varies, than the intensity of a wave is directly proportional to the square of
the amplitude and inversely proportional to the square of the distance from the energy source.
We can understand intuitively that a sound is louder the closer we are to it and softer the farther we are away from it.
If a sound source is suspended in midair so that its sound is transmitted equally in all directions, the sound energy
will spread out spherically. If the sound source is limited to a short burst, it will die out quickly. The sound is gone.
But of course, this is impossible. Once produced, the sound exists forever. But because a finite amount of sound
energy spreads over a larger and larger volume of space there is less energy per square meter. As shown inFigure
11.6, after the energy has traveled fromR 1 to 2R 1 , the sphere of energy will be spread out over four times the area.
The energy passing through each per square meter at 2R 1 will have only one-fourth the energy it did after passing
pointR 1. After the energy has traveled a distance from the source three times as great, 3R 1 , the energy will be spread
out over nine times the area. The energy passing through each square meter will have only one-ninth the energy
it did after passing pointR 1. The energy continues to spread until the amount of energy passing through each per
square meter is too small to be detected by the human ear.