Introduction to Impedance

1.3. Introduction to Impedance#

Impedance is a key concept in acoustics, describing the opposition a system presents to oscillatory motion when subjected to a driving force. Understanding impedance is critical for analyzing sound propagation, absorption, and reflection in various mediums.

What is Impedance?#

Impedance, denoted by \(Z\), is defined as the ratio of the force to the velocity in a system:

\[Z = \frac{F}{v}\]

where:

  • \(F\) is the force applied to the system.

  • \(v\) is the resulting velocity.

For harmonic motion, impedance is often represented as a complex quantity:

\[Z = Z_r + jZ_i\]

where:

  • \(Z_r\) is the real part, representing resistance.

  • \(Z_i\) is the imaginary part, representing reactance (mass and stiffness effects).

Types of Impedance#

  1. Mechanical Impedance: Resistance to motion in mechanical systems.

  2. Acoustic Impedance: Resistance to sound propagation in a medium.

Acoustic Impedance#

Acoustic impedance is defined as:

\[Z_0 = \frac{p}{v}\]

where:

  • \(p\) is the sound pressure.

  • \(v\) is the particle velocity.

In air, the characteristic impedance depends on the medium’s density \(\rho\) and the speed of sound \(c\):

\[Z_r = \rho c\]