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Acoustic Transmission

Jun 26, 2014 11:14 AM, By Bob McCarthy

Moving sound from point A to B


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Figure 1: Inverse square law: The standard transmission loss rate for sound in air (free field conditions). See larger image

Transmission is the movement of signals from senders to receivers. For acoustic transmission, the senders are musical instruments, voices, loudspeakers—anything that makes noise. The receivers are ears and microphones. Propagation through air is complex. It is noticeably frequency-dependent, begins in unique shapes, goes in all directions, bends around things, and changes with the weather. Traveling through a wire, by contrast is indoor living at its finest.

Ready to get theoretical? An infinitely small sound source will propagate spherically as an ideal point source. Sound propagates equally outward in all directions (omnidirectionality) and will exhibit an SPL loss rate of 6dB for every doubling of distance. Last week, we loaded our infinitely small speakers into the truck but nobody could find them when we got to the gig.

Waves and Sources

All sound sources have size and therefore are not ideal point sources. We can still start from the ideal single sound source propagating spherical waves and losing approximately 6dB per/doubling of distance. The directional propagation pattern will be subject to a host of steering options but for now, let’s suffice to say that once we get far enough away from the source, it will propagate with a constant directional pattern over distance.

Planar waves are an acoustic wavefront created when the source is stretched over an area. This is found at the mouth of a horn, where the wavefront has been shaped by its expanding taper. The loss rate and directionality diverge greatly from the spherical radiation model inside the area where planar radiation occurs. Propagation reverts to spherical after exiting the horn mouth. The horn’s directional imprint is maintained, but the loss rate reverts to 6dB/doubling.

Consider another theoretical construct: the infinite line source, an array of closely spaced sources of infinite length. Whereas the planar wave stretches its width in two dimensions, the infinite line source stretches in just one. In theory we can reduce the loss rate to 3dB/doubling. In practice it takes infinity to unload the truck. A finite line source creates reduced loss propagation for a finite distance, and then it reverts to the spherical propagation model of 6dB/ doubling. We see spherical propagation unless we are in the near field of an array or have our head in a horn.

Speed

The speed of sound in air formula is 331.4 + 0.607 x temperature (°C) in meters/second. This yields 344.75 meters/second at 22°C. Wrapping our brains around this is difficult because the parameters are so out of scale. Imagine a speedometer that reads kilometers per week. 334.75 meters is too big to visualize and one-second time increments are laughably imprecise.

Let’s invert and convert this to milliseconds/meter instead. That’s 2.94 milliseconds/meter (at 22°C), which can be rounded to 3 milliseconds/meter. There are three options for English system users: (1) Learn the metric system, (2) milliseconds/foot, which rounds to 0.9 milliseconds/foot and, (3) feet/milliseconds, which rounds to 1.1ft./milliseconds. I cannot emphasize enough the advantage of visualizing distance in milliseconds, since this unit is required for understanding phase and frequency, speaker interaction and reflections.

Upper and Lower Limits

An acoustic source (or loudspeaker) propagates sound into a very low impedance medium: air. The ear (or microphone) senses the propagating waveform without sucking all the air out of the room. In short, lots of power is required to push the waveform through the medium, but not to sense its presence.

At extremely high levels (>150dB SPL), the air medium becomes increasingly non-linear and hits a hard limit at 194dB SPL peak (equivalent to one atmosphere). On the rarefaction side (low pressure) we have literally run out of air. There are physical limits to the medium, not just our ears, so the quest for infinite SPL ends at 194dB SPL peak. Compression chambers and horn throats are among the most likely places where acoustic medium distortion will occur.

The lower limit is Brownian noise, which is around the same loudness as our threshold of hearing (0dB SPL). Nothing in nature actually sits still, and air molecules are no exception. Brownian motion is statistically random and therefore creates white (not brown) noise.



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