WAV-05

Characteristic acoustic impedance

Z = ρ c, and intensity I = p² / Z.

Reading speed

AcousticsRayleigh

Governing equation

Z=\rho c,\quad I=\dfrac{p^2}{Z}

where

\rho: Density (kg/m³)
c: Sound speed (m/s)
p: Pressure amplitude (Pa)
Z: Impedance (Pa·s/m)
I: Intensity (W/m²)

Lecture brief

Historical brief

d’Alembert’s wave equation, Snell, the thin-lens maker, Doppler and Bragg interference are the classical optics-and-sound toolkit. The lab is propagation, image and shift. This sheet (WAV-05 — Characteristic acoustic impedance) is the form associated with Rayleigh. Working symbols: $\rho$ , $c$ , $p$ $\rightarrow$ $Z$ , $I$ . The ratio of acoustic pressure to particle velocity in a travelling wave is the characteristic impedance ρ c of the medium.

Purpose

Purpose: compute

Z

I

from

\rho

c

p

in Waves & optics via

Z=\rho c,\quad I=\dfrac{p^2}{Z}

Z = ρ c, and intensity I = p² / Z. Use it when a real waves & optics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\rho = 1.200\,\mathrm{kg/m^{3}}

c = 343.000\,\mathrm{m/s}

p = 0.200\,\mathrm{Pa}

, the governing relation

Z=\rho c,\quad I=\dfrac{p^2}{Z}

yields

Z = 411.600\,\mathrm{Pa·s/m}

I = 9.718e-5\,\mathrm{W/m^{2}}

. Plane travelling wave, linear acoustics. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Density \rho1.2 kg/m³Sound speed c343 m/sPressure amplitude p0.2 Pa

Outputs

Impedance Z411.600 Pa·s/m
Intensity I0.000097 W/m²

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

Plane travelling wave, linear acoustics.

The ratio of acoustic pressure to particle velocity in a travelling wave is the characteristic impedance ρ c of the medium.

Reading speed

Watch on YouTube