Acoustics and Vibration Animations

Daniel A. Russell, Graduate Program in Acoustics, The Pennsylvania State University

All text and images on this page are ©2013 by Daniel A. Russell and may not used in other web pages or reports without permission.

The content of this page was originally posted on December 2, 2013.

Absorption and Attenuation of Sound in Air

Overview of Absorption

I intend to write some text explaining the general process of absorption of sound in air (viscous effects, thermal conduction effects, and molecular relaxation processes). But, in the mean time, the interactive plot below works and allows for calculation of the absorption coefficient for sound in air.

NOTE: This plot is a Computable Document Format (CDF) object created by Mathematica and you will need to install the free Wolfram CDF Player to be able to see it and interact with it. Unfortunately, the CDF player is not yet available for mobile devices.

How to Use this Interactive Plot

By moving the three sliders you can adjust the values of:

  • the relative humidity (from 0 to 100%),
  • the frequency (from 20 Hz up to 40 kHz),
  • and the temperature (from 0oC to 30oC).
If you click on one of the [+] buttons at the right of each slider, you can see the actual numerical value for that variable. You can then use the "-" and "+" buttons to decrease or increase the value in discrete steps. You should be able to type in a number into the text box (and hit the [return] key) though this may not work well on some web-browsers. The "play" button will animate the plot as a movie.

The colored curves on the plot represent the following:

  • The black dashed line represents the classical absorption due to viscous and thermal conduction effects. Viscous and thermal conduction absorption are both proportional to the square of frequency, so on a log-log plot the classical absorption looks like a straight line with a slope of 2.
  • The Red curve represents the molecular relaxation due to the Nitrogen (N2) molecules that comprise 78% of the air.
  • The Blue curve represents the molecular relaxation due to the Oxygen (O2) molecules that comprise 21% of the air.
  • The solid Black curve is the sum total of all three absorption mechanisms.
  • The two Green lines are guides to show the value of absorption (given as a number in the blue box at the upper left of the plot) for a specified frequency (selected via the Frequency slider).


  1. H.E. Bass, L.C. Sutherland, A.J. Zuckerwar, D.T. Blackstock, and D.M. Hester, "Atmospheric absorption of sound: Further developments," J. Acoust. Soc. Am., 97(1), 680-683 (1995).
  2. ANSI Standard S1-26:1995, "Calculation of the Absorption of Sound by the Atmosphere" (ISO 9613-1:1996).