Particle amplitude - Definition and Overview

Particle displacement or particle amplitude ξ is a distance measurement in m (metre) of the movement of a particle(real or imagined) in a medium as it transmits a wave. In most cases this is a longitudinal wave of pressure as with sound, but it can also be a transverse wave as with the vibration of a taut string. When applied to a sound wave through a medium of air, particle displacement would be the physical movement back and forth of a molecule of air in the direction the sound wave is travelling as it passes.

It can be represented in terms of other measurements:

<math>

\xi = \frac{v}{\omega} = \frac{v}{2 \cdot \pi \cdot f} = \frac{p}{Z \cdot \omega} = \frac{p}{Z \cdot 2 \cdot \pi \cdot f} = \frac{a}{\omega^2} = \frac{1}{\omega}\sqrt{\frac{J}{Z}} = \frac{1}{\omega}\sqrt{\frac{E}{\rho}} = \frac{1}{\omega}\sqrt{\frac{P_{ac}}{Z \cdot A}} <math>

• acoustic impedance Z in N·s/m³
• sound particle velocity v in m/s
• frequency f in Hz
• sound pressure p in N/m² = Pa
• angular frequency <math>\omega<math> = 2 · <math>\pi<math> · f
• particle displacement ξ in m
• sound intensity J in W/m²
• sound energy density E or w in W·s/m³
• sound power or acoustic power P_ac in W
• area A in m²

Particle amplitude or particle displacement is a very important linear sound field value.

See also

• Sound particle velocity
• Sound pressure
• Wave