TA Speaker Topics - Points, Line, and Plane Sources

Topic No. 7

Point, Line and Plane Sound Sources

by
John L. Murphy
Physicist/Audio Engineer

Q: Can someone explain why the SPL from a line-source falls off at -3db per doubling of distance compared to 6 dB for point sources?

It's true! Infinite line sources have the characteristic of having their SPL fall off at a rate of 3 dB per doubling of distance. This is a well known characteristic of infinite line sources. As an empirical example consider the observed behavior of the noise pollution from a highway. Folks living near highways are the unfortunate victims of the highway noise only falling at only 3dB per doubling of distance from the highway. That's because the highway noise source precisely fits the model of an infinite line source. A pretty good approximation! The engineers who battle noise know this behavior all too well. But let's look even further . . . at the behavior of a plane source. . .

What follows is a brief review of the behaviors of point, line, and plane sound sources.

Point Sources

The SPL from an ideal point source radiator falls at the rate of 6 dB per doubling of distance. The Intensity of sound from the point source falls off as the inverse square of the distance. This is known as the inverse square law. The energy radiated from the point source is evenly distributed over the surface of an expanding sphere. The surface area of the sphere is inversely proportional to the distance (radius of the sphere) squared.

Infinite Line Sources

The SPL from an infinitely long line source falls off at a rate of 3 dB per doubling of distance. This is because the energy distribution is now over the surface of a cylinder, rather than a sphere as in the case of the point source. Because the surface area of the expanding cylinder is inversely proportional to distance, NOT distance squared, it follows that the energy density falls simply with distance from the source, rather than distance squared.

Infinite Plane Sources

Imagine an infinitely large flat surface that radiates sound. The SPL from an infinitely large plane sound source is constant with distance from the source. The energy distribution from the source is now over the surface of another plane some distance from the source. As the wave propagates it does not expand but rather continues to pass through precisely the same area as the source itself. Therefore the energy density at any point in space is equal to the energy density at the source plane itself. The SPL is constant everywhere in the vicinity of a plane radiator!

Some Comments on Finite Sources

It is important to note that we have been discussing the behaviors of an infinitesimal point source and infinite line and plane sources. Real sound sources with finite geometries will exhibit different characteristics from these ideal extremes.

A finite line source will behave more as an infinite line when the observation point is very close to the line compared to its length. At greater distances the source looks more like a point radiator and the SPL will fall at 6 dB per doubling of distance.

A finite plane source likewise will exhibit constant SPL with distance only when the observation point is very close to the plane compared to the dimensions of the plane. At larger distances the finite plane source behaves more like a point radiator and the SPL will fall at 6 dB per doubling of distance.

Now, go build an infinite line array. Hint, use ceiling and floor reflections of a floor-to-ceiling line source to complete the infinite line!

jlm