Mean Free Path Length for Radiating Point Sources in Specular Reflecting Enclosures

This paper deals with the calculation of Mean Free Path Length (MFPL) especially for lower frequencies and non diffuse sound fields. Using the classical formula the MFPL is under-estimated. To show this the different spatial distributions and the methods of calculating the mean free path length are compared. Here the special case of non-diffuse sound fields is regarded.

There are several possible ways of calculating the ensemble mean. The harmonic ensemble mean is related to the mean of the impact rate. Both methods yields the MFPL for diffuse sound fields. In the case of a sphere however, and radiation from a surface point the harmonic mean leads to a physical inconsistency if a specular reflection law is assumed.

In general it can be shown for convex rooms that the arithmetic ensemble mean in case of specular reflection gives longer values than the harmonic ensemble mean. The "convexity" and thus the mean free path length of the enclosure can be regarded as dependent from the ratio of wavelength to structural dimensions of the room. For long wavelengths the room may look convex neglecting the small surfaces, even if the room is concave for small wavelengths. So, the longer reverberation times at low frequencies in many rooms can be explained even for frequency independent absorption. A formula is introduced for calculating the harmonic mean for general room shapes. Examples are derived for spherical and rectangular enclosures and compared with integral equation theory and measured results.