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Critical distance

Critical distance is, in acoustics, the distance at which the sound pressure level of the direct sound D and the reverberant sound R are equal when dealing with a directional source. In other words, it is the point in space at which the combined amplitude of all the reflected echoes are the same as the amplitude of the sound coming directly from the source (D = R). This distance, called the critical distance ${\displaystyle d_{c}}$, is dependent on the geometry and absorption of the space in which the sound waves propagate, as well as the dimensions and shape of the sound source.

In a reverberant space, the sound perceived by a listener is a combination of direct and reverberant sound. The ratio of direct sound is dependent on the distance between the source and the listener, and upon the reverberation time in [the room]. At a certain distance the two will be equal. This is called the "critical distance."

— Glenn White and Gary Louie (2005)[1]

A reverberant room generates a short critical distance and an acoustically dead (anechoic) room generates a longer critical distance.

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Transcription

People always ask me "Give me some simple ways to kind of figure out what my room sounds like?" "How much sound is my room contributing to the overall sound that I'm hearing in the room?" So I was trying to come up with some ideas that people can actually do themselves in the studio and get a handle of it. Quick stuff that doesn't take forever and tons of measuring gear and stuff. One of those items is called critical distance. Critical distance is the balancing act if you will between direct and reflected energy. We know that direct energy is the straight line energy from our loud speakers and then we also know that reflected energy is all that energy that strikes our room surfaces and bounces back. Well in Critical distance, there's a magical balance between those two numbers, between the direct and the reflected and you can find it. It takes a little practice and get your self a chair that has casters on it that you can move up and down. Move up and down the center line between your two speakers equidistance from your side walls and you'll find it. It'll be in a little 3ft area, 2 1/2 ft area in your room depending on room size, and by moving your chair up back and forths you'll get a pretty good idea of where that critical distance is. It'll also tell you about the acoustics in your room. It'll tell you what kind of reflection pattern there is in your room, what surfaces are contributing the most to reflected sound that you hear and then you can get a handle on what issues your room can possibly have. You have to live in this room, you have to work in this room and live some of us in the room because we work so much in the rooms but the bottom line is this is a quick test critical distance to kind of get a hand on how much reflection vs direct energy you room can handle. Thank you!

Calculation

The calculation of the critical distance for a diffuse approximation of the reverberant field:

${\displaystyle d_{c}={\frac {1}{4}}{\sqrt {\frac {\gamma A}{\pi }}}\approx 0.057{\sqrt {\frac {\gamma V}{RT_{60}}}},}$

where ${\displaystyle \gamma }$ is the degree of directivity of the source (${\displaystyle \gamma =1}$ for an omnidirectional source), ${\displaystyle A}$ the equivalent absorption surface, ${\displaystyle V}$ the room volume in m3 and ${\displaystyle RT_{60}}$ the reverberation time of room in seconds. The latter approximation is using Sabine's reverberation formula ${\displaystyle RT_{60}=V/6A}$.

Sources

1. ^ White, Glenn and Louie, Gary (2005). The Audio Dictionary, 3rd edition, p.89. University of Washington Press. Cited in Hodgson, Jay (2010). Understanding Records, p.36. ISBN 978-1-4411-5607-5.