Using subwoofers to improve sound quality: Part 1 - Speaker Boundary Interference

An introduction to speaker boundary interference

Deep nulls in the frequency response in the bass region can be caused by phase cancellation between the direct sound wave from a sound producing device and the indirect sound wave that has reflected from a nearby boundary such as the floor, ceiling or walls. This phenomenon is called speaker boundary interference or SBIR for short. This measurement shows an example of SBIR effects:

The frequency of the SBIR dip changes according to distance from the boundary according to the formula:

Frequency of cancellation = speed of sound / (2 x path length difference)

This relationship between cancellation frequency and path length difference can be exploited to remove SBIR effects.

How using a subwoofer can reduce speaker boundary inteference

A simplified example and picture will help illustrate both SBIR and how using a subwoofer can reduce its effects.

Take the common situation of a speaker which is placed 4ft out from the back wall as in the diagram. Using the formula introduced above we can calculate a cancellation at 71Hz due to a path length difference between the direct and indirect sound of 8ft. Now a sub is introduced into the system and a crossover point of 80Hz selected. The sub is placed 1ft from the back wall. Calculating the theoretical cancellation frequency for the sub, we see that this is at 141 282Hz. Since the sub is crossed over at 80Hz there is only limited cancellation at 141 282Hz since the frequency response is many dB down as a result of the rolloff of frequencies above the crossover point. The cancellation caused by the main speakers being 4ft out from the back wall is also reduced since the crossover is attenuating frequencies below the crossover point.

What do you think about this cunning subwoofery?

Comments

[audioblazer]

Is the math correct? Based on your eg with listener 15 ft fr back wall. Subwoofer 1 ft from the back wall. Indirect path distance 16 ft. Direct path 14 ft, so cancellation freq, 1130/ 2x 2 = 282 hz

[Nyal at Acoustic Frontiers]

Hi Audioblazer - wow you are quite right...not sure how I missed that...thanks!

For readers - I have updated the article to reflect the correct cancellation frequency of 282Hz.