Free Field

Almost all sound reduction testing and calculations are undertaken with diffuse sound fields on both sides of the wall. In this case, the sound is incident on the wall at all possible angles of incidence. However, there are many instances in real life where sound arrives at the panel at a single angle of incidence and the transmission loss is somewhat different from the diffuse field case. INSUL can predict the performance of single panels (not double or triple panels) at a single angle of incidence. This is most significant at high frequencies around the coincidence/critical frequency.

From INSUL version 7.0, INSUL can predict the sound reduction of a single panel (such as glazing) at particular angles of incidence. This is relevant to a situation where the sound source is outdoors (in a free field) and the sound arrives at the window at a single angle of incidence and could be quite important in a situation where the sound is incident on the partition at near grazing incidence. But first, we must overcome a conundrum. In classical acoustic theory, the sound transmission loss (aka sound reduction index) is defined as the ratio of incident intensity to transmitted intensity. At 90° incidence, the incident intensity goes to zero (because the projected partition area at 90° is zero), but the sound transmission index also goes to zero. So how much sound is transmitted?

Rindel (1995) has proposed an alternative definition that avoids these problems and enables straight forward calculation of the transmitted noise. Rindel has proposed a definition of the external transmission loss ($R_E$) that uses the ratio of energy densities on both sides of the partition instead of incident intensity. For an incident plane wave, the energy density is related to the spatial average of the sound pressure squared, while on the receiver side the sound field is assumed to be diffuse and the energy density is again related to the sound pressure squared. Thus on both sides of the wall, the quantities are easily measurable and calculatable.

$$R_E = 10\log_{10}\left(\frac{<p_S^2>S}{<p_R^2>A}\right)$$

where:

• $p_S$ is the sound pressure on the source (free field) side
• $p_R$ is the sound pressure on the receiver side (diffuse field)
• $S$ is the area of the wall
• $A$ is the equivalent absorption area in the receiving room

Note

The energy reflected from the panel is included in the value $p_S$.