The Intensity of Three-Dimensional Waves:

 A two-dimensional sound wave looks like a series of concentric circles that get bigger as they move further away from their origin. These circles are called wavefronts. In real life, sound waves grow in three dimensions. Three-dimensional waves move out in all directions away from their origin in wavefronts that are concentric spherical surfaces. The space in between wavefronts is the wavelength. Rays indicate the motion of a set of wavefronts. Rays are lines perpendicular to the wavefronts that originate at the source of the sound and follow the wavefronts outward. If the sound is emitted evenly in all directions, the energy at a distance r from the source will be uniform on the spherical shell. If we let P equal the original power the sound has when emitted from the source, the intensity per unit area (the surface area of a sphere is the denominator) at a distance r from the source will be: The intensity level of sound is measured in decibels (dB). Decibels are units of intensity that are based upon a logarithmic scale. This means that a sound with an intensity of 20 dB is ten times as loud as one with an intensity of 10 dB, 30 dB is ten times as intense as 20 dB, and so on. The reason for this logarithmic scale is that humans hear intensity on a similar logarithmic scale. So, while a 20 dB sound is ten times as intense as a 10 dB sound, we perceive it as only twice as loud. The hearing threshold (level at which humans begin to perceive sound) is 0 dB. When a sound reaches upwards of 120 dB, it is above the threshold of pain (point at which most people begin feeling pain). Everything in between can be heard by a human with normal hearing. But, these levels aren't constants. What a human perceives as loud or soft depends on the frequency as well as the intensity of the sound. The graph below displays intensity levels compared with the frequencies for sounds of equal loudness for humans. The bottom line is the threshold of hearing. At a 1 kHz frequency, the hearing threshold is 0 dB, but at 60 Hz the decibel level is 50. Only one percent of all human beings can hear sounds this low, so, the lower line is mainly for those with very good hearing. The next line up is the hearing threshold for the majority of people. The top line is the pain threshold. Other than at one point, about 4 kHz, this line varies little. All of the other lines also dip down at 4 kHz. We can gather from this graph, then, that the human ear is most sensitive at about 4 kHz.