Particle acceleration

This article is about small-scale particle acceleration in acoustics. For acceleration of charged particles to very high energies, see particle accelerator.

In acoustics, particle acceleration is the acceleration (rate of change in speed and direction) of particles^{[clarification needed]} in a sound transmission medium. When sound passes through a medium it causes particle displacement^[1] and as such causes changes in their acceleration.

The acceleration of the air^{[dubious – discuss]} particles of a plane sound wave is given by: $${\displaystyle a=\delta \cdot \omega ^{2}=v\cdot \omega ={\frac {p\cdot \omega }{Z}}=\omega {\sqrt {\frac {J}{Z}}}=\omega {\sqrt {\frac {E}{\rho }}}=\omega {\sqrt {\frac {P_{\text{ac}}}{Z\cdot A}}}}$$

Symbol	Units	Meaning
a	m/s^2	particle acceleration
v	m/s	particle velocity
δ	m, meters	particle displacement
ω = 2πf	radians/s	angular frequency
f	Hz, hertz	frequency
p	Pa, pascals	sound pressure
Z	N·s/m^3	acoustic impedance
J	W/m^2	sound intensity
E	W·s/m^3	sound energy density
Pac	W, watts	sound power or acoustic power
A	m^2	area

See also

• Sound
• Sound particle
• Particle displacement
• Particle velocity

References

1. Arthur Schuster (1904). An Introduction to the Theory of Optics. London: Edward Arnold. An Introduction to the Theory of Optics By Arthur Schuster.

External links

• Relationships of acoustic quantities associated with a plane progressive acoustic sound wave - pdf