How much comparable power do we need for different frequencies?

[Sokel]

What I see is the instruments in the midrange have momentarily dropped out for that snippet...

I can do this all day long. Perhaps the OP can shed more light on his actual question...(?)

Chris

I think REW draws accurate picture for peaks:

That's classical so not an extreme example.

 

[Chris A]

One interesting subject I've run into: when you look at a fairly capable loudspeaker--the Klipschorn--that can easily output almost undistorted music (and transients) at extremely loud levels (and no, that's not really why people buy these loudspeakers in my experience), you might have missed the fact that the K-77 tweeters used for many decades can only handle 4w "music power". If you try to put 5w average music power through the K-77 tweeter (actually an ElectroVoice T-35 tweeter that has passed QC inspection at Klipsch), you'll fry the voice coil/diaphragm. The midrange and woofer drivers can absorb at least 10x that level (while playing unbelievably loud) without damage.

I think the OP is probably trying to understand this phenomenon.

Chris

 

[Sokel]

...and that's an extreme,Pan Sonic:

 

[Chris A]

That's classical so not an extreme example.

This from Chapman's 1996 JAES article:

I think you're trying to catch some fog here...

Chris

 

[DVDdoug]

For example, let’s say we have a 90db/1mt sensitivity speaker. So;
How much power do we need to get
90db/1mt and 100db/1mt at 20hz?
90 and 100db at 30hz?
90 and 100db at 40hz?

+10dB is 10 times the power.
dB = 10 x log(P/Pref).

Or for voltage, dB = 20 x log(V/Vref). (Power is the combination of voltage & current and with a given impedance load current is proportional to voltage... If you double one you also double the other.)

...I have these formulas in a spreadsheet, as well as the reverse formulas for converting dB to power and voltage ratios.

The "power needed" for 90dB doesn't depend on frequency.

But "power handling" is does depend on frequency because there's more energy in the low frequencies. It's the (short-term) average power that burns-out speakers, not the peaks.

Also, with real world program material, the more octaves a driver has to handle, the more power it has to handle.

Let’s say, both tweeter and subwoofer has 90db sensitivity. But these sensitivity numbers are measured in different frequencies. At least it’s not the sensitivity of all frequencies. It’s generally sensitivity of 1khz for many speakers.

If you're talking about a speaker system (a complete 2-way or 3-way speaker), ideally the frequency response is flat. If the tweeter has higher sensitivity, the crossover network usually has resistors to knock it down to match the other driver(s). ...You usually don't build a speaker with a woofer that's more sensitive than the tweeter because you need power & SPL in the bass range so the last thing you want to do is knock-down the bass to match a low-sensitivity tweeter.

If the bass falls-off and you boost the bass by +6dB to make it "flat", that's 4 times the power.

Of course, woofers have lower sensitivity at high frequencies and tweeters have lower sensitivity at low frequencies. The specs for the individual drivers are usually NOT at 1kHz.

This is averaged. You miss the peak values, very valuable for knowing the power needed.

In Audacity you can use high-pass, low-pass, and band-pass filters. Then you can "trick" it into giving the peaks by running the Amplify effect. Amplify will default to whatever amplification (or attenuation) is needed for maximized/normalized 0dB peaks. For example, if Amplify defaults to a change of +10dB, your peaks are currently -10dB. (Then you can cancel the effect since you just want to check.) Or, there are some plug-ins that will measure peak & RMS and maybe 3rd-party plug-ins for LUFS.

If you are building a bi-amped or tri-amped speaker, you'd want to know the typical peak ratios for the different drivers.

 

[Sokel]

This from Chapman's 1996 JAES article:

View attachment 402532

I think you're trying to catch some fog here...

Chris

See,the experimental admittedly,but still music (for some) that follows.
The CD has even more extreme examples.

 

[Hayabusa]

What I see is the instruments in the midrange have momentarily dropped out for that snippet...

And the conclusion about estimated power is?
Any constructive answer?

 

[Hayabusa]

I think REW draws accurate picture for peaks:

View attachment 402531

That's classical so not an extreme example.

Peaks in time....... Not in the spectrum

 

[Sokel]

Peaks in time....... Not in the spectrum

In spectrum,look at the axis.
Just throw the file in RTA with the right settings and REW will do the rest,4 charts,two for average (each channel) and two for peaks.
They will appear in the main window after it's done analyzing them (you can watch the process in the meantime in RTA )

 

[Hayabusa]

In spectrum,look at the axis.
Just throw the file in RTA with the right settings and REW will do the rest,4 charts,two for average (each channel) and two for peaks.
They will appear in the main window after it's done analyzing them (you can watch the process in the meantime in RTA )

What I mean: to answer the question about power you need to look at the peaks in TIME in the spectrum, so for instance how it looks in the 'waterfall' view in audacity.

this will show you the amplitude per frequency in time.

An amplifier that takes only a part of the spectrum must be able to handle the peaks not the average spectrum over the whole track.

 

[Hayabusa]

In spectrum,look at the axis.
Just throw the file in RTA with the right settings and REW will do the rest,4 charts,two for average (each channel) and two for peaks.
They will appear in the main window after it's done analyzing them (you can watch the process in the meantime in RTA )

I now see what you mean...

I missed the context switch to REW

 

[Sokel]

What I mean: to answer the question about power you need to look at the peaks in TIME in the spectrum, so for instance how it looks in the 'waterfall' view in audacity.
View attachment 402540

this will show you the amplitude per frequency in time.

An amplifier that takes only a part of the spectrum must be able to handle the peaks not the average spectrum over the whole track.

Ok,now I get what you're saying and you're right of course.
Although,you can eyeball the time in REW too during the process but that's as rough as it gets,is only an indicator.

 

[kemmler3D]

So, I can't find the appropriate graph for some reason, but there are several factors that point in the direction of bass needing more power in an audio system than treble.

1. Low frequencies require more air to be displaced to produce the same SPL, which increases power requirements.
2. Human hearing is less sensitive at very low frequencies, which increases the amount of bass we put into recordings to have the same perceived loudness, which increases power requirements, which partly explains why all the music histograms are heavily weighted toward bass
3. Low frequency drivers are typically less sensitive than high frequency drivers, which further increases power requirements for bass

So it all adds up to why you may only need 1-2w for 20khz and 1200w for 20hz.

 

[Jumu]

So, I can't find the appropriate graph for some reason, but there are several factors that point in the direction of bass needing more power in an audio system than treble.

1. Low frequencies require more air to be displaced to produce the same SPL, which increases power requirements.
2. Human hearing is less sensitive at very low frequencies, which increases the amount of bass we put into recordings to have the same perceived loudness, which increases power requirements, which partly explains why all the music histograms are heavily weighted toward bass
3. Low frequency drivers are typically less sensitive than high frequency drivers, which further increases power requirements for bass

So it all adds up to why you may only need 1-2w for 20khz and 1200w for 20hz.

This is what I’m trying to learn. I saw some topics that people say that they only need 5-10watts to drive their speakers. So why do we need thousands of watts for subwoofers. ( I know we need

Thank you everyone. You are very helpful. But I still couldn’t find an answer.

Is there any “general rule” of rational relationship between power and frequencies?

I know all logarithmic relationships between power and spl but it doesn’t work same for all frequencies maybe because of perceived loudness effect. I don’t know.
If yes, there should be a general formula.

Additionally, it’s clear that the power needed to move a 1” tiny tweeter and 18” big woofer is not the same.

I am not capable of calculating with measurements tools. So a general formula is what I am looking for.

Thank you all for your time.

 

[Chris A]

Actually, there are a couple of things working against you at low frequencies below 100 Hz:

1) the efficiency of loudspeakers decreases rapidly below ~100 Hz due to the difference in size of the diaphragm to wavelengths generated, and
2) the efficiency of the human hearing system also decreases rapidly below 100 Hz (as seen in the Equal Loudness contours you posted)

So what I've found is that the empirical relationship is still about -15.5 dB/decade (or ~5.1 dB octave) based on SPL. You can use the table found to right at this link to convert amplitude ratios into power ratios.

First you have to achieve flat response with your loudspeakers (i.e., the loss of "sensitivity" or efficiency of woofer and subwoofers have to be compensated for via higher electrical drive levels--usually through crossover balancing network design or active loudspeaker EQing. [Then you have to achieve ~5.1 dB/octave (built into the music itself) to hear a balanced presentation--which I mentioned above].

That's how you get to talking about thousands of watts of electrical power driving very inefficient direct-radiating woofers and subwoofers. You really need to keep increasing the size/efficiency of loudspeaker bass bins and subwoofers to avoid the thousands-of-watts situation, since thermal compression (due to almost instantaneous voice coil heating to red hot levels) and air compression (woofer diaphragms losing their acoustic effectiveness due to their small dimensions relative to the acoustic wavelengths being generated). Horn-loaded (including and especially "tapped horn") bass bins are usually overlooked, but necessary to keep your deep bass from rapidly "fading" due to thermal heating effects.

Chris

 

[DVDdoug]

1. Low frequencies require more air to be displaced to produce the same SPL, which increases power requirements.

2. Human hearing is less sensitive at very low frequencies, which increases the amount of bass we put into recordings to have the same perceived loudness, which increases power requirements, which partly explains why all the music histograms are heavily weighted toward bass

It also gets a little "weird" because when SPL is measured with an SPL meter it's usually A-Weighted which is a rather crude approximation of the equal loudness curves (or one equal loudness curve, since it's the same at all volume levels). With A-weighting, the bass (and high frequencies) measures lower to more-closely measure how we hear it.

But if you are using REW and a measurement mic, you are measuring flat (accurately) with no weighting.

3. Low frequency drivers are typically less sensitive than high frequency drivers, which further increases power requirements for bass

If you are buying a speaker, it's up to the manufacturer to make it "flat" (within cost and size constraints, etc.). That means the power requirements are only related to program material (and any EQ adjustments you make), NOT the sensitivity of the drivers.

If you are building a full-range speaker, it's up to you to knock-down the signal to the tweeter (and midrange if any) if necessary to match the woofer. Some power to the midrange and tweeter is wasted, but it's power you don't need. If the power wasn't wasted the frequency response would be messed-up with (relatively) boosted mids & highs.

Active speakers are usually bi-amped or tri-amped. That allows the levels going to the drivers to be separately calibrated. The gain of the tweeter and midrange can be turned-down (if necessary) so everything matches and there is usually a bigger amp for the woofer. Also, EQ is often built-in to flatten and extend bass response. Any EQ bass boost WILL require more power, but again that's up to the speaker manufacturer.

Active subwoofers also often have EQ built-in to extend the bass response.

Subwoofers often need more power than the main speakers (but I don't know "the formula".)

 

[dualazmak]

I assume ADOBE Audition's 3D gain-Fq-time spectrum does help you in terms of discussion here;
- An Attempt Sharing Reference Quality Music Playlist: at least a portion and/or whole track being analyzed by 3D color spectrum of Adobe Audition
- https://www.audiosciencereview.com/...by-3d-color-spectrum-of-adobe-audition.47103/
We can play and listen to the music on the 3D spectrum with the moving/proceeding vertical yellow cursor!
(In my setup, while watching/monitoring also by the 12-VU-Meter Array...)

Also IEC 60268-17 compatible VU-Meter Array does help on real time monitoring of various Fq zones;
- My nostalgia and preference for large glass-face VU meters: DIY of 12-VU-Meter Array in multichannel multi-driver multi-way multi-amplifier stereo audio system: #535
- NISHIZAWA R-65 VU meter plus ATV205EXT VU amp board is compatible with IEC 60268-17 VU meter specification/standard: #545
- Dancing video of my IEC 60268-17 compatible large glass-face DIY 12-VU-Meter Array
_____Part-1: with "High Frequency Linearity Check Track" of Sony Super Audio Check CD: #750
_____Part-2: with typical "Full Orchestra Music"-1: #751
_____Part-3: with typical "Full Orchestra Music"-2: #752
_____Part-4: with typical "Jazz Piano Trio Music": #753


Edit: Just for example, like this YouTube video clip (quickly prepared today) shows.
Please note the camera captured VU-Meter Array view and the soundtrack are not fully synchronized with the screen captured software views due to my quick preparation of this example video; I believe, however, you can easily understand what I mean in this post. Please visit here #753 for sync video clip of VU-Meter Array.

 

[dualazmak]

If you are interested in actual AC electricity power consumption of amplifier(s) in VAC and/or Watt scale, you can use a clamp-on current meter/tester like I shared here.
- Apparent power consumption of whole audio system during daily audio listening sessions: how SDGs-friendly is it? (not the idle power, please.)

Spoiler

If needed, you can measure each of the amplifiers' live power consumption driving subwoofer(s), woofers, midranges, tweeters and super-tweeters in case of multichannel multi-SP-driver multi-amplifier fully active setup like my audio rig.

 

[Holmz]

Here is a cumulative spectrogram ("plot spectrum") from Audacity of Steely Dan's Reelin' in the Years (demastered and upwards expanded to approximately studio recorded dynamics):

View attachment 402502

Does this answer your question?

Chris

Generally those FFT plots sort of show next to nothing, although this one offers some hope.
We really need to pick some band of frequencies and integrate over the bins.

I have always heard that for general music, 50% of the power is in the woofer, 35% in the midrange, and 15% in the tweeter.

Looking at ^that^ FFT, one can sort if see it being reasonable.

 

[Jumu]

1) the efficiency of loudspeakers decreases rapidly below ~100 Hz due to the difference in size of the diaphragm to wavelengths generated, and
2) the efficiency of the human hearing system also decreases rapidly below 100 Hz (as seen in the Equal Loudness contours you posted)

Yes Chris, thank you. To my knowledge, these are the main reasons (there maybe more, which I dont know

Now, we have to find a good mathematician to create a general formula for this