Jun 26, 2014 11:14 AM, By Bob McCarthy
Moving sound from point A to B
Loss Rate (Inverse Square Law)
The inverse square law is the common name for the 6dB/doubling loss rate of spherical wave propagation. This hypothetical standard rate (the “free field” response) requires special conditions that can never quite be met, but nonetheless, are the best starting reference for mapping out level over distance. Air is a lossy medium in the HF range, which falls at an accelerated rate. Reflected energy adds to the direct sound, which (mostly) reduces the loss rate. Coupled speaker arrays (sources close together) can decrease the loss rate (as a combination), but only in the near field. Inverse square is not just a good idea. It’s the law. It doesn’t discriminate between loudspeakers, musical instruments, and humans.
A trend is seen as we move away from a typical source (more HF directionality than LF). The HF region will maintain free field behavior for a longer distance than the LF. Low frequencies go rogue first because their wide coverage quickly gets the floor, ceiling, and walls involved, reducing the loss rate. The HF has three advantages that keep it in the free field zone for longer: more directionality in the source, higher loss rate in the air, and more absorption on the surfaces.
In summary: Air loss accelerates the loss rate linearly with distance. Reflections decelerate the loss rate minimally in the near field and increasingly in the far field. Speaker arrays decelerate the loss rate maximally in the near field and minimally in the far field.
As we walk away from a sound source the frequency response will change, since the highs will drop at closer to the free field rate than the lows. This is true of loudspeakers and natural sources.
Does coverage pattern affect the inverse square law? Does an omnidirectional device drop off at a different rate than a directional one? The answer is a slightly qualified “no.” Once we are far enough away for the source’s coverage pattern to fully stabilize, the drop-off rate follows the inverse square law rules. If it’s 10dB louder in front at 1 meter, it will hold that relationship at further distances. Spherical wave propagation is an equal opportunity pressure dropper.
How do we know when we are far enough to have a stable loss over distance over angle? This is a case where size matters. A tiny point source like a clicker will reach maturity at close range. A giant Japanese Taiko drum needs some space. Spread sources (e.g., a piano) or those with multiple acoustic outputs (e.g., bagpipes) also add complexity. A typical two-way speaker is both spread and has multiple outputs. A 5-meter-tall stack of speakers will need lots of room to finish adding up the elements.
Air is a highly imperfect transmission medium, and adding weather to the equation does nothing to make our lives easier. The dynamic nature of air leads to changes in frequency response, sound speed, and directional pattern.
The air medium’s accelerated HF loss rate generally tracks with humidity. Dry air is lossy air. Unless we are doing outdoor concerts in January in Oslo, we will find a simple relationship between humidity and HF loss, without the need to consider temperature. The frequency response effects are like a low-pass filter. The filter slope rises as humidity falls and the corner frequency falls as transmission length increases. Humidity effects on the HF response are easy to hear, and easy to act on. They affect only the very top end so a broad HF boost or cut can return things back to normal.
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