Acoustic Impedance Calculator Formula

Understand the math behind the acoustic impedance calculator. Each variable explained with a worked example.

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Formulas Used

Acoustic Impedance

impedance = density * sound_speed

Variables

VariableDescriptionDefault
densityMedium Density(kg/m3)1.225
sound_speedSpeed of Sound(m/s)343

How It Works

Characteristic Acoustic Impedance

Acoustic impedance determines how much sound pressure results from a given particle velocity in a medium.

Formula

Z = rho * c

  • *rho* = medium density (kg/m3)
  • *c* = speed of sound in the medium (m/s)

    • Air: about 415 Rayl. Water: about 1.48 million Rayl. Large impedance mismatches cause strong reflections at boundaries.

    Worked Example

    Air at sea level (rho = 1.225 kg/m3, c = 343 m/s).

    density = 1.225sound_speed = 343
    1. 01Z = rho * c
    2. 02Z = 1.225 * 343
    3. 03Z = 420.2 Rayl

    Frequently Asked Questions

    Why does impedance mismatch cause reflections?

    When a sound wave hits a boundary between two media with different impedances, part of the energy is reflected. The greater the mismatch, the more reflection. This is why sound barely penetrates from air into water.

    How is acoustic impedance used in medical ultrasound?

    Different tissues have different impedances. Reflections at tissue boundaries create the contrast in ultrasound images. Coupling gel is used to reduce the air-skin mismatch.

    What are the units?

    Rayl (Pa s/m) in SI. One Rayl equals one pascal-second per metre. Named after Lord Rayleigh.

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