## Fundamental Acoustics

Sound is the result of varying pressure waves within a medium, usually air.  Audible sound, that which is detectable by the human ear, is due to very small rapid changes in the air pressure above and below atmospheric pressure.  The range of acoustic pressure is from approximately 0.00002 Pa to 10 Pa. To illustrate the sensitivity of the human ear, at the low pressure end, a displacement of the ear drum as small as the diameter of a hydrogen atom can be audible. An animation by Dr. D Russell, shown below, illustrates the one dimensional wave propagation down a tube.  The speed at which sound propagates is known as the speed of sound and is given as approximately 344 m/s at standard temperature. The audible variations in pressure occur between approximately 20 to 20,000 times per second which translates to a frequency range of 20Hz to 20kHz.  Frequency is the number of pressure variations per second and is measured in Hertz (Hz). Knowing the speed and frequency of a sound we can determine the wavelength, or distance from one peak on a wave to the next corresponding peak.

Given the large range of audible pressure, sound is usually expressed on a logarithmic scale instead of the normal pressure unit of Pascals.  When expressed in this manner, amplitude of sound is called a sound pressure level (SPL) and has the units of decibel (dB).  A logarithmic measure is mostly used to compare a quantity of interest to a reference value, often the smallest likely value of the quantity, in the case of sound, the threshold of hearing.  The reference value used to convert acoustic pressure to a decibel is 0.00002 Pa.  Bruel & Kjaer has provided an illustration that shows the relationship between sound pressure and sound pressure level.

Sound pressure levels are not arithmetically additive and must be logarithmically added.  That is, 50 dB plus 50 dB is not equal to 100 dB.  The equation to add decibels is given as: More to come later