Relation between Power and Frequency

[DougL]

Double post

 

[weltersys]

You’re missing the point. I understand very well the impact of the sensitivity and even the impedance. What I need to understand is the relationship with the ACTIVE crossover frequency. That’s why I said “all parameters being equal”. The only thing I want to change is the low frequency crossover. So if I need 100W for my mids when the crossover is at 80 Hz, how much power would I need if I set the crossover at 160 Hz? 50 W?

Ghyduart,

Assuming equal sensitivity and a flat impedance curve throughout the frequency reproduction range, the peak power (voltage) needed for a given SPL is identical for all frequencies.

Looking at a 1/3 octave RTA (real time analyzer) one can see both the average and peak distribution, cymbal splashes can peak just as high as a kick drum or a vocal fundamental.

The average power distribution in music will be genre (and song) dependent, there is no mathematical formula which will tell you where the average or peak power demands are greatest.

Art

 

[mark100]

You’re missing the point. I understand very well the impact of the sensitivity and even the impedance. What I need to understand is the relationship with the ACTIVE crossover frequency. That’s why I said “all parameters being equal”. The only thing I want to change is the low frequency crossover. So if I need 100W for my mids when the crossover is at 80 Hz, how much power would I need if I set the crossover at 160 Hz? 50 W?

Yes. moving the xover up in freq will lower power needed for the mids (and raise power needed for the lows).

But I doubt you could ever calculate the amount of power reduction anywhere near correctly for an actual speaker.

You could however measure it, driver-by-driver, with a pair of averaging true RMS, voltmeter and ammeter.

 

[jolathe]

These sorts of questions were bugging me too initially. I ended up writing a C program that would read through a wave file and calculate the voltage, current, amp power and sound pressure level for each driver in an active system with a given crossover/equalization setup and set of drivers. I even ran it for all the 3,000 or so songs in my collection to get an idea of the average and extreme results. When I built my system, I found out that the "how much power" question doesn't really matter, the typical per channel amplifier sizes can produce output way too excessive for neighbors, significant others, and ears in an active system.

 

[weltersys]

Yes. moving the xover up in freq will lower power needed for the mids (and raise power needed for the lows).

Mark,

Moving the crossover frequency up or down simply changes the average power used for the various driver's bandpass.
Assuming one wants the same peak SPL from each bandpass (assuming equal sensitivity), the same voltage swing (amplifier "power") is needed for each band, regardless of how little average power is consumed in the band.

Art

 

[Pano]

...there is no mathematical formula which will tell you where the average or peak power demands are greatest.

No there isn't. So you need to think about headroom. You can look at a lot of music tracks (100s or 1000s) to get a general idea of averages and peaks. I've done that and posted the results, they were linked to earlier in the thread. You do need to mind the peaks and headroom, but to my surprise the peaks also fall off with increasing frequency, much like the average power. The midrange can be particularly peak heavy.

 

[mark100]

Mark,

Moving the crossover frequency up or down simply changes the average power used for the various driver's bandpass.
Assuming one wants the same peak SPL from each bandpass (assuming equal sensitivity), the same voltage swing (amplifier "power") is needed for each band, regardless of how little average power is consumed in the band.

Art

Hi Art, yes voltage swing needs to stay the same.

But isn't power, voltage times current?

So, the wider the bandwidth being produced at any given voltage, the more the current needed.

The lower the frequency of the bandwidth being produced, the more the current needed. (at any given voltage and all things such as sensitivity etc, being constant)

And I respectfully submit that power commonly means average power.

 

[GM]

I’ve always heard that if you put white noise into a speaker at 100 watts the point at which 50 watts will be below a frequency and 50 watts above is at 200hz.
In other words, 200hz is the 50/50 point in power needed in a system.

Don't know, but sound power is exponential, so the mean for the OP's 80-2560 Hz = [80*2560]^0.5 = ~452.5 Hz, 160-2560 Hz = ~640 Hz or 2^0.5 = ~1.4142x higher, though none of this is relevant for other than choosing driver size/XO points IME.

IOW, using Doug's chart, the mean power = only ~22.63 W/633.72 Hz with no way to extrapolate that some symphonic CDs have [clipped] +30 dB transients in the ~250-500 Hz octave that require 1 kW minus the speaker system's peak power handling capability; so as previously noted, electrical power for a given bandwidth [BW] is chosen based on continuous average and dynamic headroom SPL required @ 'x' distance with ideally a bit more to ensure the amp's not driven outside its linear BW.

GM