Is 100 Watts at 8 Ohms same as 100 Watts at 4 Ohms?

I have an old home theater system, for some of it's speakers it says 100W at 4 Ohms, for some other speakers and subwoofers it says 100W at 8 Ohms. Is this same? Or is there some mischief going on.

 

W=IV
I=V/R
.: W=V*(V/R) = V^2/R
.: V = (W*R)^-1 As R changes for the same W, V changes
So to reach the same 100W for different impedance speakers the voltage changes.

 

W=IV
I=V/R
.: W=V*(V/R) = V^2/R
.: V = (W*R)^-1 As R changes for the same W, V changes
So to reach the same 100W for different impedance speakers the voltage changes.

In terms of sound quality and loudness will they be different?

 

100W is 100W but it could be pure noise... Has nothing to do with quality.

 

Loudness is the same if the speaker efficiencies (watts to sound intensity) are the same.
They may not be.

 

But why would they go with different Ohms for different speakers?

 

To suit the power supply voltage available.

 

The 100W/4Ω amplifier gives 20V rms output. If you connect an 8Ω sepaker to it, you will get 50W, and it will be 3dB quieter*.
The 100W/8Ω amplifier gives 28V rms output. If you connect a 4Ω speaker to it, you will overload it.

*If it is an amplifier with a switched-mode power supply. An older amplifier with a 50Hz transformer will give slightly more power because the power supply voltage will rise at low load, so perhaps you might get 65W and it will be only 2dB quieter.

The sensitivity of speakers will vary from about 84dB @1W@1m for a tiny pathetic modern one in a tacky plastic case, made as cheaply as possible, to about 115dB @1W @1m for a horn-loaded enclosure from the 1960s.

 

But why would they go with different Ohms for different speakers?

Marketing.

 

Marketing.

It wasn't mentioned on the box, it was mentioned in the manual. If it was for marketing, wouldn't it be displayed on the box.

 

It wasn't mentioned on the box, it was mentioned in the manual. If it was for marketing, wouldn't it be displayed on the box.

In that case, I'd suggest "misprint" - the likelihood is that all the amplifiers run off the same power supply.