Home Speaker Asylum

General speaker questions for audio and home theater.

Some rough calculations

216.192.10.12

I have no rule of thumb, but an example might illustrate the important parameters.

Assume an auditorium with around 500 seats and a volume of 2500 m^3.
Assume a reverberation time of 1.5 s, which corresponds to a 20% average sound absorption coefficient for the room surfaces. Let's say the speaker has a directivity gain of 3, corresponding to 10 dB.

With the voume V, reverberation time T60, and speaker gain G, we can calculate the critical distance Xr from the speaker for which the direct SPL equals the reverberant SPL in the room.

Xr = 0.1 sqrt(G V /(pi T60)) = 4 m

If the speaker has a power sensitivity of 90 dB/1W at 1m, then the direct SPL will be 90 - 20log(Xr/1m) = 78 dB at 4 m, where it will be equal to the reverberant SPL anywhere in the room. So 1 W from this loudspeaker will get you 78 dB at 10 m or 20 m.

A 100 W amplifier will give 20 dB more, or a direct SPL of 110 dB at 1 m, 84 dB at 20 m. The reverberant SPL will be 110-12 = 98 dB, and at 20 m it will be 98-84 = 14 dB higher than the direct SPL.

You can find more detail under the link to my site and in modes1.xls .
SL




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