Quick maths problem.

[wonko]

You're right about the power of 2 relationship assumption, but your linear relationship is an assumption too.
I think it should really be a log relationship between power and sound pressure, and then some other relationship between sound pressure and perceived volume.
This link https://geoffthegreygeek.com/amplifier-power/ suggests that 4 times the power only gives about 50% increase in perceived volume.

 

[Avenged7Fold]

OP - Plot the graph of power in Watts and volume but have a logarithmic volume (dB) axis. That should make things clearer and give you a nice straight line relationship if I recall correctly. This is the sort of thing you are after.

I think your wording has confused us all. Do the above and i guarantee you will get somewhere

 

[johnloo]

v^(p* t)
V = volume
P= original power
t= 1-.25

 

[dl8860]

Not sure where the squaring is coming from in the above examples, given the information in the question.

The op clearly describes a formula that looks like this:

4P = 2V (four times the power results in twice the volume). For the purposes of this question it could be being assumed to be linear.

Therefore is you reduce the left hand side by 25% you have to reduce the right hand side by 25%. Reducing by 25% is the same as having 75% remaining.

0.75 x 4P = 0.75 x 2V
3P = 1.5V

Is what the formula ends up as.

Although it's not clear what the exact question is, I would say the answer is that if you reduce the power by 25% you end up with one and a half times the original volume.

The squaring also achieves the 'four times the power is double the volume'. So do a variety of other more complicated relationships between volume and power.

 

[banja]

Its not the exact science I'm looking at and I'm not looking for the proper physics of the amp situation - I just wanted to get the approximate % via the maths. So, assuming four times the power equals twice the perceived volume, what % of 100% volume would 75% power equal. Simples!

 

[dl8860]

The only relationship that fits your description of 'four times the power equals twice the volume', for all values of V and P is P=V^2, as below


So, let's take a certain value of P. You want to take 75% of that P, and work out the corresponding Volume decrease.

If we start at P = 4096, the corresponding V is 64. If you take 75% of 4096, that gives you 3072. P = V^2, so V is root(P) = 55.4. That's 0.86% of the original value, a decrease of 13.4%.

If we start at P = 16, then V here is 4. If you take 75% of 16, that's 12. Here, V is 3.46. That's 0.86% of the original value again, confirming the decrease is 13.4%.

This is basically the same as Wonko said in post #11, but just a bit more illustrated

 

[Django x2]

This is like trading shares. If a Share valued at £100 goes up %100 it's now worth £200. If it falls by 100% the next day it's worth £0

 

[banja]

The only relationship that fits your description of 'four times the power equals twice the volume', for all values of V and P is P=V^2, as below


So, let's take a certain value of P. You want to take 75% of that P, and work out the corresponding Volume decrease.

Thanks to everyone for contributing. Sorry if my explanations were crap. And props actually to Geforce for being ti first to suggesting 86%/13%

If we start at P = 4096, the corresponding V is 64. If you take 75% of 4096, that gives you 3072. P = V^2, so V is root(P) = 55.4. That's 0.86% of the original value, a decrease of 13.4%.

If we start at P = 16, then V here is 4. If you take 75% of 16, that's 12. Here, V is 3.46. That's 0.86% of the original value again, confirming the decrease is 13.4%.

This is basically the same as Wonko said in post #11, but just a bit more illustrated

Yes, thanks! As I said, my crude X Y plot of power vs volume came out at about the 85 mark, so I think this is definitely correct

Not sure who got to the answer first, but thanks all for contributing. Sorry if my explanations were crap.