Speaker sensitivity, impedance, and calculating amp power

It’s not always about educating or helping the OP, as many will read this thread but fewer actually contribute in a positive way other than to ascribe a narrow view , perhaps just personal bias.

we in the business of helping studios, bands, mastering engineers, recording artists and audiophiles start with a discussion of target SPL. Most people, including on this venerable free admission site don’t actually own an accurate SPL meter or have any idea how loud a trumpet is from
say 30’ ?

so OP, let’s start there, how loud ?

The 2nd question, so you can get started on it is: what is the spectral density of the music you listen to ?

fewer still own and pay attention to a RTA ( real time analyzer )

a current “ client “ of mine ( pro bono ) is using three tracks to evaluate potential systems and size his speaker/amplifier...

the difference in spectral density is off the charts different and proof he does not need a subwoofer... just well engineered full range speakers.. 

Question 3 is about duty cycle....

is that “ word salad “ enough ?

its easy but math and science based...

OP:

If you are interested in theory alone, start with understanding power and sensitivity (not efficiency) at 1 meter.

Assume the amplifier is a perfect voltage source, and the speaker an ideal 8 ohms. Then understand that you can use the power in dB to tell you the difference in speaker output.

dB louder = 10 log (power / 1 watt)

So, if you h ave an 89 dB sensitive speaker, and apply 100 watts, the output at 1 meter will be 109 dB.

The truth is that an ideal speaker with flat frequency response speaker has equal voltage sensitivity at all frequencies, but the power consumed at any frequency is proportional to the inverse of the impedance, so the idea of using power to determine output is a cheat. We’re really using the amps equivalent voltage difference.

So long as your speaker is exactly 8 Ohms, then we can use the power calculation (above) interchangeably with the voltage calculation, below:

db louder = 20 log ( voltage / 2.83V)

The real problem we have is that amps are not sold by voltage output, but by power, but in fact, power amps are not power amps at all, they are voltage amps with (ideally) zero output impedance. That is, a power amplifier does not multiply the input power. It multiplies the input voltage and produces whatever current, and therefore power, is needed.

I’m overfilling your bucket here because I want you to reconsider your question. :)

This handy Wikipedia entry may further confuse you:  https://en.wikipedia.org/wiki/Decibel


Best,

E

Avoid any speaker that dips below 4 ohms through the bass section.Above 5-6 ohms is even better.The flatter the impedance curve the better.