# Practical course: Measurement of the absorption in Kundt's tube

## Introduction

The sound absorption property of a material is described by its absorption coefficient $&alpha$. It is defined as the ratio of absorbed and incident sound intensity. $&alpha$ lies between 0 and 1 and is strongly frequency dependent. There are two common measurement methods:

## Reverberation chamber

The measurement in the reverberation chamber uses the relation between absorption, volume and reverberation time according to Sabine's formula.

## Kundt's tube

For the measurement of the absorption under normal sound incidence, Kundt's tube can be used (Figure 1). Kundt's tube serves to create a one dimensional plane wave sound field at discrete frequencies. For that purpose a loudspeaker located at one end of tube generates a sine wave. This wave propagates in the tube to the other end and will be reflected at the hard termination. Thereby the incident and reflected sound wave form an interference pattern with pressure maxima and minima. By introducing absorbing material in front of the hard termination, the reflection is reduced and as a consequence the sound pressure maxima decrease and the minima increase. As will be shown below, the absorption coefficient can be determined from the ratio of maximum and minimum sound pressure alone.

The sound field in the tube is sensed by a microphone that can be moved along the tube axis. With pr as sound pressure of the reflected wave and pe as sound pressure of the incident wave one can write:

The sound pressure maxima and minima in the standing wave are formed by constructive and destructive interference of the incident and the reflected wave:

From the ratio

the absorption coefficient is calculated as

The JavaScript below simulates the microphone voltage for different measurement configurations in Kundt's tube. First of all, a sample configuration and an exciting frequency have to be selected. Then the sound field can be sensed at an arbitrary position in the tube by help of the navigation buttons. The field microphone voltage shows the corresponding quantity that is proportional to the sound pressure RMS value.

a: the absorption coefficient of a foam sample of 3 cm thickness shall be determined in the two configurations:
1. foam directly in front of hard termination
2. foam with a distance of 10 cm to hard termination
for the frequencies 125 Hz, 250 Hz, 500 Hz, 1 kHz and 2 kHz.

b: In many cases knowledge of the absorption coefficient is sufficient. However, the measurement in Kundt's tube allows in principle to evaluate phase information as well. For the frequencies 250 Hz and 1 kHz the phase turn of the reflection shall be determined in case of the foam mounted directly in front of the hard termination.

c: For the arrangement of the open tube the resulting sound field shall be observed and discussed. Of special interest is the strength of the reflection. What is the explanation of the phenomenon?

## Simulation of Kundt's tube

Sample:

frequency:

microphone position, x coordinate [cm]: microphone voltage [Volt]: