Sound pressure

In air, sound pressure can be measured using a microphone, and in water with a hydrophone.

The SI unit of sound pressure is the pascal (Pa).

Together, they determine the sound intensity of the wave.

Sound intensity, denoted I and measured in W·m−2 in SI units, is defined by

where Acoustic impedance, denoted Z and measured in Pa·m−3·s in SI units, is defined by[2]

where Specific acoustic impedance, denoted z and measured in Pa·m−1·s in SI units, is defined by[2]

where The particle displacement of a progressive sine wave is given by

where Taking the Laplace transforms of v and p with respect to time yields

, the amplitude of the specific acoustic impedance is given by

Consequently, the amplitude of the particle displacement is related to that of the acoustic velocity and the sound pressure by

If the sound pressure p1 is measured at a distance r1 from the centre of the sphere, the sound pressure p2 at another position r2 can be calculated:

Sound pressure level (SPL) or acoustic pressure level (APL) is a logarithmic measure of the effective pressure of a sound relative to a reference value.

Sound pressure level, denoted Lp and measured in dB,[4] is defined by:[5]

where The commonly used reference sound pressure in air is[7] which is often considered as the threshold of human hearing (roughly the sound of a mosquito flying 3 m away).

The proper notations for sound pressure level using this reference are Lp/(20 μPa) or Lp (re 20 μPa), but the suffix notations dB SPL, dB(SPL), dBSPL, and dBSPL are very common, even if they are not accepted by the SI.

[8] Most sound-level measurements will be made relative to this reference, meaning 1 Pa will equal an SPL of

In other media, such as underwater, a reference level of 1 μPa is used.

Most sound level meters provide readings in A, C, and Z-weighted decibels and must meet international standards such as IEC 61672-2013.

While 1 atm (194 dB peak or 191 dB SPL)[11][12] is the largest pressure variation an undistorted sound wave can have in Earth's atmosphere (i. e., if the thermodynamic properties of the air are disregarded; in reality, the sound waves become progressively non-linear starting over 150 dB), larger sound waves can be present in other atmospheres or other media, such as underwater or through the Earth.

Human hearing does not have a flat spectral sensitivity (frequency response) relative to frequency versus amplitude.

Humans do not perceive low- and high-frequency sounds as well as they perceive sounds between 3,000 and 4,000 Hz, as shown in the equal-loudness contour.

Because the frequency response of human hearing changes with amplitude, three weightings have been established for measuring sound pressure: A, B and C. In order to distinguish the different sound measures, a suffix is used: A-weighted sound pressure level is written either as dBA or LA.

B-weighted sound pressure level is written either as dBB or LB, and C-weighted sound pressure level is written either as dBC or LC.

Unweighted sound pressure level is called "linear sound pressure level" and is often written as dBL or just L. Some sound measuring instruments use the letter "Z" as an indication of linear SPL.

[13] The distance of the measuring microphone from a sound source is often omitted when SPL measurements are quoted, making the data useless, due to the inherent effect of the inverse proportional law.

In the case of ambient environmental measurements of "background" noise, distance need not be quoted, as no single source is present, but when measuring the noise level of a specific piece of equipment, the distance should always be stated.

Because of the effects of reflected noise within a closed room, the use of an anechoic chamber allows sound to be comparable to measurements made in a free field environment.

[13] According to the inverse proportional law, when sound level Lp1 is measured at a distance r1, the sound level Lp2 at the distance r2 is

The formula for the sum of the sound pressure levels of n incoherent radiating sources is

in the formula for the sum of the sound pressure levels yields