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# Using math to figure out how loud my speakers would be?

Over the last few days I've been trying to determine whether my proposed 50W receiver (Marantz NR1603 or similar) would be powerful enough to drive the Pioneer SP-FS52 tower speakers I'm hoping to get. The majority of the answers seemed to have been yes, maybe, and no ... so I'm still trying to figure things out and I decided to turn to my good friend math to solve the problem.

However, since I'm not an acoustic expert I wanted to get feedback on this to make sure I'm not making some stupid assumptions or mistakes.

So here goes the math:

The speakers have a 87db sensitivity at 2.83V and are 6ohms. That means that they produce 87db at 1m when being driven with 1.33W (2.83V @ 6ohms = 0.47amps | 2.83V * 0.47amps = 1.33W). Doing some wonderful logarithmic math we see that going from 1.33W to 50W increases our sound output by 15.75db to 102.75db. However, that's at 1 meter away. I will be sitting 8 feet away or 2.43 meters. Again doing some math we figure out that this increase in distance will drop our db by 7.7db to 95db. Now assuming the exact same sound is being played by both left and right speakers we add 3db to the total volume bringing us to 98db.

So in the end I know that if I put 50W of power into these speakers I will get 98db from them at my sitting distance. Does all this make sense?

Now to figure out if 98db is loud enough without a db meter

Thanks,
Harry

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Quote:
Originally Posted by Harry Muscle

Over the last few days I've been trying to determine whether my proposed 50W receiver (Marantz NR1603 or similar) would be powerful enough to drive the Pioneer SP-FS52 tower speakers I'm hoping to get. The majority of the answers seemed to have been yes, maybe, and no ... so I'm still trying to figure things out and I decided to turn to my good friend math to solve the problem.

However, since I'm not an acoustic expert I wanted to get feedback on this to make sure I'm not making some stupid assumptions or mistakes.

So here goes the math:

The speakers have a 87db sensitivity at 2.83V and are 6ohms. That means that they produce 87db at 1m when being driven with 1.33W (2.83V @ 6ohms = 0.47amps | 2.83V * 0.47amps = 1.33W). Doing some wonderful logarithmic math we see that going from 1.33W to 50W increases our sound output by 15.75db to 102.75db. However, that's at 1 meter away. I will be sitting 8 feet away or 2.43 meters. Again doing some math we figure out that this increase in distance will drop our db by 7.7db to 95db. Now assuming the exact same sound is being played by both left and right speakers we add 3db to the total volume bringing us to 98db.

So in the end I know that if I put 50W of power into these speakers I will get 98db from them at my sitting distance. Does all this make sense?

Now to figure out if 98db is loud enough without a db meter

Thanks,
Harry

If you want clean sound, then I would subtract 3 db, so you are not running the AVR at it's limit. Power compression may rob you a little bit, but not much, since you are now talking about only 25 watts out of the AVR.
you also need to consider that that 50W max output is at 8ohm. at 6 ohm it is rated for a max of 80W
87dB/2.83v/m, 2.43m, 47 watts into 8 ohms & 62 watts into 6 ohms will produce 96dB per one speaker or 99dB per 2 speakers.

The \$300 Denon 1612/1613 can output 118.5 WPC into 8 ohms x 2Ch, 141.5 WPC x 2 Ch into 4 ohms.

74 watts/8 ohms & 98 watts/6 ohms will produce 98dB/1 speaker or 101dB/2 speakers.

If the speaker is all or mainly 8 ohms, then 118 watts into 8 ohms could produce 100dB/1 speaker or 103dB/2 speakers.
Edited by AcuDefTechGuy - 11/10/13 at 6:48pm
Quote:
Originally Posted by Harry Muscle

So in the end I know that if I put 50W of power into these speakers I will get 98db from them at my sitting distance. Does all this make sense?
Almost. First off, you want 6dB of headroom, so a realistic figure of how much power you'll be delivering is 12.5w. If you really need 50w continuous output you want at least a 200w/ch amp. That takes you down to 93dB, but in practical terms that's probably plenty. However, there are two errors in your calcs. The inverse square rule applies in an anechoic space. In a room you can figure a 3 to 4dB loss per doubling of distance from the source will be closer to the actual. And two speakers driven with the same voltage level produce 6dB more than one.
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