Sound pressure

Sound pressure p (acoustic pressure) is the measurement in pascals of the average sound wave pressure variations of a sound wave passing by a fixed point. The symbol for pressure is the lower case p. (The upper case P is the symbol for power. Often you find this misprinted.)

<math>

p = \frac{F}{A} \ \mathrm{ \ or \ } \ \frac{F}{S} <math>

p = sound pressure in Pa = pascal = N/m²

F = force in newton N, and A = area in m² or S = surface.

The SI unit is pascal with the symbol Pa. One pascal equals a pressure of one newton per cm²

<math>

1 \ \mathrm{ Pa = 1 \frac{N}{\, m^{2}} } = 1 \mathrm{ \frac{kg}{\, m \cdot s^{2}} }\;<math>

The amplitude of sound pressure decreases in the free field (direct field) with 1/r of the distance of a point source.

The sound pressure level is calculated in dB as:

<math>

L_p=20\, \log_{10}\left(\frac{p_1}{p_0}\right)\mathrm{dB} <math>

Reference sound pressure is: p₀ = 2 · 10^-5 Pa = 20 µPa

Sound pressure p in N/m² or Pa is:

<math>

p = Z \cdot v = \frac{J}{v} = \sqrt{J \cdot Z} <math>

Z: acoustic impedance, sound impedance, or characteristic impedance, in N·s/m³

v: acoustic velocity, sound velocity, or particle velocity, in m/s

J: acoustic intensity or sound intensity, in W/m²

Notice: The often used term "intensity of sound pressure" is not correct. Think it over. Use "magnitude", "strength", "amplitude", or "level" instead. "Intensity" is the quadratic sound energy value, but "pressure" is a linear sound field value. Intensity is not pressure.

The sound pressure p is connected to particle displacement or particle amplitude ξ, in m, by:

<math>

\xi = \frac{v}{2 \cdot \pi \cdot f} = \frac{v}{\omega} = \frac{p}{Z \cdot \omega} = \frac{p}{Z \cdot 2 \cdot \pi \cdot f} <math>

where:

Z: acoustic impedance, in N·s/m³

v: sound velocity, in m/s

f: frequency in Hz

p: sound pressure, in N/m² = Pa

ω: angular frequency = 2π·f

Sound pressure p:

<math>

p = \rho \cdot c \cdot \omega \cdot \xi = Z \cdot \omega \cdot \xi = {\xi \cdot Z \cdot 2 \cdot \pi \cdot f} = \frac{a \cdot Z}{\omega} = c \cdot \sqrt{\rho \cdot E} = \sqrt{\frac{P_{ac} \cdot Z}{A}} <math> normally in units of N/m² = Pa.

where:

ρ: density of air

c: speed of sound

ω: angular frequency = 2π·f

ξ: particle displacement (particle amplitude)

Z: acoustic impedance (characteristic impedance) = c · ρ

a: sound power or acoustic power

A area

See also: Sound pressure level