@kijanki
Yes, I of course realize that there are two speakers. But for a listener at a centered position that is equidistant from the two speakers the calculation I provided, involving the difference in SPL at 10 feet vs. 1 meter, applies just as well. Obviously it is not usually possible to be 1 meter in front of both speakers at the same time, but if we hypothetically assume that to be possible (so that we can use the speaker’s specified or measured sensitivity, which of course is based on 1 meter) my calculation of the **difference** in SPL between 1 meter and 10 feet is not affected. All that would be affected is the absolute value of the SPL at the two distances, which the second speaker would cause to increase by the same amount at both distances.
In other words, the second speaker does not compensate for 3 db of the distance-related loss. It just increases the reference point to which that loss applies.
Here is the calculation of the 9.68 db difference in SPL that I stated occurs between listening distances of 1 meter and 10 feet, putting aside the effects of room reflections:
If we denote the two distances as D1 and D2 a loss of 6 db per doubling of distance corresponds to a loss of 20 x log(D1/D2).
1 meter is 39.37 inches; 10 feet is 120 inches.
20 x log(120/39.37) = 9.68 db
For your 3 meter listening distance the result would be:
20 x log(3/1) = 9.54 db
Factoring in 3 db or so of room gain brings that loss close to the 6 db figure you cited. Although that amounts to a 6 db error in Benchmark’s rule of thumb guideline, since their guideline asserts that essentially no loss would result.
Best regards,
-- Al
Yes, I of course realize that there are two speakers. But for a listener at a centered position that is equidistant from the two speakers the calculation I provided, involving the difference in SPL at 10 feet vs. 1 meter, applies just as well. Obviously it is not usually possible to be 1 meter in front of both speakers at the same time, but if we hypothetically assume that to be possible (so that we can use the speaker’s specified or measured sensitivity, which of course is based on 1 meter) my calculation of the **difference** in SPL between 1 meter and 10 feet is not affected. All that would be affected is the absolute value of the SPL at the two distances, which the second speaker would cause to increase by the same amount at both distances.
In other words, the second speaker does not compensate for 3 db of the distance-related loss. It just increases the reference point to which that loss applies.
I’m sitting at about 3m from the speakers equal to loss of a little more than 6dB (9.5dB?). Rule of thumb has -3.5dB error here, but works perfectly for 2m listening distance.
Here is the calculation of the 9.68 db difference in SPL that I stated occurs between listening distances of 1 meter and 10 feet, putting aside the effects of room reflections:
If we denote the two distances as D1 and D2 a loss of 6 db per doubling of distance corresponds to a loss of 20 x log(D1/D2).
1 meter is 39.37 inches; 10 feet is 120 inches.
20 x log(120/39.37) = 9.68 db
For your 3 meter listening distance the result would be:
20 x log(3/1) = 9.54 db
Factoring in 3 db or so of room gain brings that loss close to the 6 db figure you cited. Although that amounts to a 6 db error in Benchmark’s rule of thumb guideline, since their guideline asserts that essentially no loss would result.
Best regards,
-- Al