Sound Power Intensity Pressure

Overview

Engineering reference data for Sound Power Intensity Pressure in acoustics.

Key Formulas

Speed of Sound

$c = \sqrt{\gamma R T}$

Speed of sound in an ideal gas.

Sound Level

$L = 10 \log_{10}(I/I_0)$

Decibel level.

Wavelength

$\lambda = c / f$

Wavelength = speed / frequency.

Variables

Symbol	Description	Unit
$c$	Speed of sound	m/s
$L$	Sound level	dB
$\lambda$	Wavelength	m
$f$	Frequency	Hz

Additional Relationships and Properties

Sound Intensity and Pressure Relationship

The acoustic intensity $I$ is related to the root-mean-square (rms) sound pressure $p$ and the characteristic acoustic impedance of the medium $\rho c$ (where $\rho$ is density and $c$ is speed of sound) by: $I = \frac{p^2}{\rho c}$ This relationship is crucial for connecting measurements made with pressure microphones to intensity calculations.

Inverse Square Law

For a point source radiating sound power $W$ uniformly into a free field, the sound intensity $I$ decreases with the square of the distance $r$ from the source: $I = \frac{W}{4\pi r^2}$ This demonstrates that the Sound Intensity Level $L_I$ decreases by approximately 6 dB each time the distance from a point source is doubled.

Practical Note on Sound Pressure Level

A key practical consequence derived from formula (4) is that a doubling of sound pressure ($p_2 = 2p_1$) results in a 6 dB increase in Sound Pressure Level: $\Delta L_p = 20 \log_{10}(2) \approx 6.02 \ \text{dB}$ This "6-dB rule" is a fundamental reference for assessing changes in loudness perception and acoustic exposure.

References

• Original Source