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#### kryptonitewhite

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If you cut the frequency in 1/2, why don't you need to double the excursion to maintain the same SPL?

#### FOH

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It's not a linear relationship, it's exponential.

#### FOH

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You double the diagonal picture size, you increase the picture by 4x

#### Bill Fitzmaurice

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You double the voltage, you quadruple the power. There are very few linear relationships in audio.

#### kryptonitewhite

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OK, so first we must double voltage, quadruple power, to maintain the same SPL.

Human hearing, is there an average roll off?

#### FOH

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Quote:
Originally Posted by Bill Fitzmaurice /forum/post/19636177

You double the voltage, you quadruple the power. There are very few linear relationships in audio.

Maybe you can explain. Voltage has a directly proportional relationship to power.

P=IE

1200w=(10a)120v

2400w=(10a)240v...doubles voltage, doubles power

1200w=(5a)240v.....doubles voltage, halves current, same power

Help me out here

#### LTD02

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substitute e/r for i and you get power = e^2/r

#### profundus-sanus

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Quote:
 Originally Posted by FOH Maybe you can explain. Voltage has a directly proportional relationship to power. P=IE 1200w=(10a)120v 2400w=(10a)240v...doubles voltage, doubles power 1200w=(5a)240v.....doubles voltage, halves current, same power Help me out here
your forgetting resistance. when you do that your resistance is going up significantly. 120/10 = 12 ohms, 240v/10a = 24 ohms

100v @ 1 ohm = 10kw= (100^2/1)

200v @ 1 ohm = 40kw= (200^2/1)

400v @ 1 ohm = 160kw= (400^2/1)

#### kryptonitewhite

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Quote:
 Originally Posted by profundus-sanus your forgetting resistance. when you do that your resistance is going up significantly. 120/10 = 12 ohms, 240v/10a = 24 ohms 100v @ 1 ohm = 10kw= (100^2/1) 200v @ 1 ohm = 40kw= (200^2/1) 400v @ 1 ohm = 160kw= (400^2/1)
Prof, you got a build log? Do you HT?

#### DL86

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Quote:
Originally Posted by LTD02 /forum/post/19636742

substitute e/r for i and you get power = e^2/r

Its a lie that equation!

A speaker is not a resistor.

You got to look at reactive(Q), real(P) and complex power(S).

#### Bill Fitzmaurice

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Quote:
Originally Posted by DL86 /forum/post/19638935

Its a lie that equation!

A speaker is not a resistor.

You got to look at reactive(Q), real(P) and complex power(S).

Dude, chill.

If you double the voltage into a load, be it resistive, inductive, capacitive or, as is the case with a speaker, a combination of all three, power will quadruple.

#### Starkiller4299

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Quote:
Originally Posted by Bill Fitzmaurice /forum/post/19639306

Dude, chill.

If you double the voltage into a load, be it resistive, inductive, capacitive or, as is the case with a speaker, a combination of all three, power will quadruple.

Precisely.

Any load can be modeled by it's impedance and phase at every frequency. When dealing with a specific frequency, you simply select that particular impedance and can treat it just like resistance
.

#### FOH

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Quote:
Originally Posted by Bill Fitzmaurice /forum/post/19639306

Dude, chill.

If you double the voltage into a load, be it resistive, inductive, capacitive or, as is the case with a speaker, a combination of all three, power will quadruple.

I understand your point, and I realize your reference is audio, however a 120 watt light bulb exists as a 120 watt load, regardless of voltage across it. The amperage/voltage fulcrum teeters back and forth, but the power does not change with the voltage across it.

A 1 mega-watt load for a commercial building, exists at 13,800v at the service entrance point, and the same wattage load exists at the 208/120 switch gear at the load side of the transformers. The meters that measure the wattage, do not care what voltage manipulation occurs downstream.

So to state that a doubling of voltage, results in a quadrupling of power, isn't necessarily true

Maybe I'm crazy, I'm digging out of a hell of a snowstorm

#### Starkiller4299

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FOH--most light bulbs are simple resistors, not constant power devices. So the 2 x V = 4x P still applies, as the resistance remains constant. This attribute is what allows us to install dimmers on incandescents--flourescents are an entirely different animal
.

Some motors may be modelled as constant-power, drawing whatever current is needed to make up for a lagging voltage, but you'll find that a vast majority of electrical loads offer a constant impedance.

Transformers do of course add to the fun, but simple Ohms Law manipulations tell you that all the same rules apply. If you double the voltage via a transformer but keep the impedance constant, the power will still increase by a factor of 4. The Primary (or supply) side current will reflect this chance as well.

Useful equations:

P=I^2*R

V=I*R

P=I*V

P=V^2/R

From that last equation you can easily see that with a given load, power is a quadratic of voltage. Hope that helps--I'm not looking forward to my driveway!

#### FOH

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I am crazy, and dont have the time to give to this, more later,

I stand corrected

#### noah katz

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Quote:
Originally Posted by kryptonitewhite /forum/post/19636094

If you cut the frequency in 1/2, why don't you need to double the excursion to maintain the same SPL?

At the same voltage and half the freq, the cone velocity is halved; it's taking twice the time to move the same distance.

The pressure waves which are sound are generated by velocity, so to maintain the same velocity at half the freq, displacement must be doubled.

But why velocity? After puzzling over this, I think it makes sense.

The way to create pressure in air is to get the molecules closer together, and absent a closed container the way to do this is push them fast enough so that they don't have time to move out of the way.

#### kryptonitewhite

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noah, I think i agree with you, but what I am hearing you say is double the displacement for half the frequency...which is what I would have guessed it should be, but the rule is 4X, no?

#### noah katz

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Quote:
Originally Posted by kryptonitewhite /forum/post/19642592

noah, I think i agree with you, but what I am hearing you say is double the displacement for half the frequency...which is what I would have guessed it should be, but the rule is 4X, no?

Right, I didn't finish - if the cone moves at twice the velocity for twice as long, the displacement is 4X.

#### LTD02

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"Its a lie that equation!"

lol. you are right. i was simply answering foh's question.

noah, this picture is confusing to me. it shows an arbitrary frequency (black) and 1/2 the frequency (red).

i used 4 times the excursion for the amplitude. since voltage drives the excursion, that would require 4 times the voltage. from ohm's law, p=e^/r, 4 times voltage is 16 times power. that much i understand.

what i don't understand looking at this picture is why those two waves have the same spl??? it's just re-asking krypto's question another way.

#### noah katz

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Quote:
Originally Posted by LTD02 /forum/post/19643221

what i don't understand looking at this picture is why those two waves have the same spl??? it's just re-asking krypto's question another way.

I believe if you plotted the corresponding velocities for the two waves they would have the same amplitude.

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