# Sound Pressure

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## Sound pressure

The incremental variation in the static pressure of a medium when a sound wave is propagated through it. Sound refers to small-amplitude, propagating pressure perturbations in a compressible medium. These pressure disturbances are related to the corresponding density perturbation via the material equation of state, and the manner in which these disturbances propagate is governed by a wave equation. Since a pressure variation with time is easily observed, the science of sound is concerned with small fluctuating pressures and their spectral characteristics. The unit of pressure commonly used in acoustics is the micropascal (1 μPa = 1 μN/m^{2} = 10^{-5} dyne/cm^{2} = 10^{-5} μbar). One micropascal is approximately 10^{-11} times the normal atmospheric pressure. *See* Pressure, Pressure measurement, Wave motion

The instantaneous sound pressure at a point can be harmonic, transient, or a random collection of waves. This pressure is usually measured with an instrument that is sensitive to a particular band of frequencies. A concept widely used in acoustics is “level,” which refers to the logarithm of the ratio of any two field quantities. When the ratio is proportional to a power ratio, the unit for measuring the logarithm of the ratio is called a bel, and the unit for measuring this logarithm multiplied by 10 is called a decibel (dB). The sound intensity, which describes the rate of flow of acoustic energy (acoustic power flow) per unit area, is given by the mean square pressure divided by the acoustic impedance, defined as the product of the medium density and compressional wave speed. *See* Decibel, Sound, Sound intensity

## Sound Pressure

the additional pressure developed during the passage of a sound wave through a fluid or gaseous medium. In propagating through a medium, the sound wave creates condensations and rarefactions that produce additional variations in the pressure with respect to the average pressure in the medium. Thus, sound pressure is the variable part of the pressure—that is, the fluctuations of pressure relative to the average value at a frequency corresponding to the frequency of the sound wave.

Sound pressure is a fundamental quantitative characteristic of sound. The unit of measurement for it in the SI system of units is the newton per sq m (N/m^{2}); the unit previously used was the bar (1 bar = 10^{−1} N/m^{2}). The sound level, which is the ratio, expressed in decibels, of the given sound pressure *p* to the threshold value *p*_{0} = 2 × 10^{−5} N/m^{2}, is sometimes used to characterize sound. The number of decibels is *N* = 20 log (*p*/*P*0).

The sound pressure in air varies over a wide range—from 10^{−5} N/m^{2} close to the threshold of audibility to 10^{3} N/m^{2} for very loud sounds, such as the noise of jet airplanes. Sound pressures up to 10^{7} N/m^{2} are produced in water at ultrasonic frequencies of the order of several megahertz by means of focusing radiators. The phenomenon of fluid discontinuity, or cavitation, is observed at high sound pressures. Sound pressure should be distinguished from acoustic radiation pressure.