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Basic question about sound.
Posted by Chris Jensen [IP: 32.97.92.1] on May 21, 1999 at 16:58:38
Using Mozilla/4.0 (compatible; MSIE 4.01; Windows 95):
In Reply to: Basic question about sound. posted by Robin Chen on May 19, 1999 at 18:38:09:
No offense, but some of the previous posts have provided incorrect information. Here are some facts about sound intensity (decibels, dB, SPL, W/m^2), and a review of some basic electrical concepts.electrical power: P=EI
Ohm's law: E=IR
If you wire two speakers in series, then the current through each speaker is halved, and also the voltage across each speaker is halved. The power through each speaker is 1/4 of what would be through a single speaker, so the total power delivered by the amplifier at a given voltage is 1/2. If you wire the speakers in parallel, the volatge across each speaker is the same as a single, and the current through each speaker is also the same, so the total power delivered by the amp is 2x at a given voltage. Now, there are a few things about audio amps that need to be mentioned. 1)They have a maximum voltage output. 2)They have a maximum current output. A typical amp at 8 ohms and higher is railing out its voltage supplies to deliver its maximum rated power (actually it's not quite maxed out, since rated power is for a particular maximum distortion level, so the amp has more voltage capacity than its 8ohm power rating indicates, but we will stick to the simplified case). When you look at the specs for most amps, they will show that the rated power at 4 ohms is less than 2x the rated power at 8 ohms...why is that? because of point number 2 above, they run out of current capacity before they reach their max voltage into the lower resistance. So, wiring speakers in parallel will not always get your amp to deliver 2x the power, and if your amp is not up to the task (like wiring 2 martin logans in parallel) it may even fry itself and the speakers, or at the very least it will sound bad and then shut itself down from thermal overload. Now, sound intensity.
I = W/m^2, dB = 1/10 * logI/Io, Io = 10^-12 W/m^2.
Speakers are transducers that convert electrical energy into sound energy. Within reasonable limits they have a linear power response. Double the input power, double the output power. An earlier poster was correct in noting that doubling the pressure quadruples the intensity (I = rho*v*omega^2*smax^2, deltaPmax = v*rho*omega*smax, so I is proportional to pressure squared) however, if you have two speakers at one watt you do _not_ get twice the pressure of one speaker at one watt, what you get is twice the power, which means you get 1.414x the pressure, and 3dB more intensity. 3dB is about the smallest increase in overall sound intensity that is perceptible by a person. 10 dB (10x power) is percieved as a doubling in sound intensity. Finally, to answer your question.
In theory, hooking two speakers in series and then doubling the voltage to them will produce twice the power, and increase the volume 3dB. In practice, you cannot double the voltage, so you will get half the total power since you doubled the resistance (P=V^2/R), and you will _decrease_ the volume by 3dB. The very cheapest way to get louder sound, is to sit closer to the speakers (for a sphere A = 4*pi*r^2, so I is proportional to 1/r^2). If you sit 3 feet away instead of 10 you will get a little more than 10dB increase...twice as loud.
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