Reflection and Transmission of Acoustic Waves

Watch the reflection and transmission of a simple rectangular pulse as it impinges on a boundary that separates two media having differing density and velocity. The ratios of these parameters are set with the sliders, and the animation proceeds with the current settings. For density and velocity ratios both equal to 1, no reflection occurs; for a density or velocity ratio equal to zero, no transmission occurs.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

A plane acoustic wave impinging normally on a straight boundary between two media (1 on the left and 2 on the right) will both reflect back and also transmit to the adjacent medium. The pressure amplitudes of the reflected and transmitted waves are controlled by the impedance ratio of the two media. Impedance is given by , where is the density and is the velocity. The expressions for the pressure amplitudes of the reflected and transmitted waves, for an impinging wave from the left (medium 1, ), are:
.
Divide through by to get
.
Thus, the amplitudes are controlled by the density ratio and the velocity ratio. For instance, for , the reflection coefficient approaches +1 and the transmission coefficient approaches 2. For , the reflection coefficient approaches and the transmission coefficient approaches 0. The pulse duration of the transmitted wave depends on the velocity ratio, becoming shorter if the velocity on the right is less than that on the left and, conversely, becoming longer if the velocity on the right is greater than that on the left. Depending on the density and velocity ratios, the amplitude of the reflected wave can be positive or negative. The amplitude of the transmitted wave always has the same sign as that of the impinging wave.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.