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Ofcourse there are equations that allow you to caculate the "input power required to drive a certain set of speakers at different SPL levels at different distances from the listener" in an anechoic room using a test tone.

It is exactly these equations along with some (though not complete in my view) actual testing that manufacturers use for their published figures.

A speaker that can very easily produce 110db using 200W of power (23db) at say 400Hz might not do the same at 40Hz.

Ok you have a very valid point.. So far i could not find a mathematical equation that relates Frequency of input signal to SPL and hence Power required. Any pointers in that direction....

There will be no single equation anywhere. The thing is very very application specific - wave nature of sound; fast, but not unpercievably fast speed; different properties of different material surfaces ...

there are so many variable that nobody puts his effort into actually making formula - just build and test.


If you are so interested you will have to study properties of horns and membranes, impedance matching for wave propagation between different materials and then some electrical engineering (or relevant physics).

Best is - just enjoy the music.

While I have not found any equations that can effectively tell me all I need to know about a loudspeaker I dont share Vina's view. Given the computer power available today I am sure there will be simulations available with many manufacturers (KEF, B&W, etc have their own labs and smaller manufactuers can sub-contract this work to external labs).

Amen, Navin! It is always possible to string together each factor and simulate the whole chain by seeding constants and iteratively solving the equation (the heart of simulation) at different frequencies. The closeness with which reality can be simulated depends on how fine we split the individual factors and how accurately we are able to specify the substitute values for the ones that we lump. The picture that emerges (by representing the data as a visual representation) will represent end-to-end behaviour.

Improving the repeatability, reliability and accuracy of the result is an adventure by itself, as one has to iteratively do that for each factor in the equation. That is where the locha is: to know whether we are accurate or not, the value of each factor in the equation has to be physically verified (cross checked by conducting a physical experiment with reliable instrumentation!). Simulation only helps in reducing the time taken for iteratively producing the result map that mimics reality.

I am sure parts of the factorization and physical experimentation have been done so far in PhD subjects. When we say "we haven't seen an equation so far" we only mean no one so far has taken it up in an integrated manner because of the technical and economic infeasibility / desirability. The alternate method, as KEF, B&W, et al would do is to reuse 'trusted / proven factors' and limit themselves to research on 'single / limited variation' of untrusted / unproven factors - a widely used and more economically efficient research method.

Simulations are not closed form equations. Nor are they so easy that anybody with no knowledge of sound propagation can use them. Also they cost MONEY - I don't think our friend here has the kind of money these things require. Without any packages a commercial MATLAB license costs 1.5Lacs/year and they don't give student licenses in India - I called last year and checked. More specialized software will cost a lot more.

Also even if such packages are available, he is talking about straddling two very different domains - electro-magnetics and sound wave propagation. That kind of packages are very hard to get and use.



Read my post again, I said no generic one-size-fit-all equations will be available and any equations will be application specific (which is what a simulation is). High end sound system designers have tools (usually developed in-house) which they will not share, and you can go to them but ... really, can YOU go to them?

Wow Audio Science is interesting.. but as i dig deeper and deeper i have begun to realize that the field is is more complicated that it looks (Ok so all you will say.. I told you so..). For eg: I just found that the sensitivity figures quoted by the driver manufactures is actually meaningless for any practical calculations or reference. But there seems to be a way to calculate the actual sensitivity based on reference effeciency. And guess what the.. Focal 33V2 which is rated with a sensitivity of 90db actually has a sensitivity of about 86db.

Also the earlier myth that i had that higher the sensitivity the better for the setup was blown to bits thanks to Hoffmans Iron Law.

Its like someone just opened a door and pushed me into the Amazon jungle.. Its crazy, but seems to be fun.

It is an amazing science - - for example speakers installed on the flap covering the boot space of a hatch get a deeper response, not because the speakers are better, but because the empty boot gives resonance.

If you want to really do it after learning, you'll realise that money may be better spent on the materials lining the car surfaces (mats, doors, seat covers) than on the speakers themselves - all of these things absorb sound significantly.


Anyway, if you are enjoying it my suggestion is to start with the basics - any good junior-college (11th/12th class) physics book will give a very good foundations within 2 chapters. Once you have done that - resonance, frequency response etc. and their relations to other variables (size of the speakers, surface properties ) will become very clear and the laws you are quoting here will start coming across merely as applications of those basics rather than any hard/fast laws.

It takes all of a couple of hours on a weekend.

hmmm....how do I say this....

A speaker-designer will usually have in mind a sound signature. Based on this sound signature they will consider any number of drive units that are reliable, consistent and relatively hardy. The more eclectic designers are more willing to experiment with 'diffcult' drive units. Occasionally large companies like Harman Kardon employ designers like Kevin Voecks (ex-Snell Acoustics) to produce a product line (in this case Revel) with a unique indentity but usually these designers (like Jim Thiel, David Wilson, Richard Vandersteen, John Dunlavy, John DeVore, Jacques Mahul etc...) go it alone.

The sound-signature will more often that not result in a flagship speaker. The flagship will then be used as a reference and a team of brand managers and bean counters will decide price points and a line will develop based on the flagship.

As far as the tools used..well quite obviously the bigger companies have anechoic labs equipped with scores of microphones and test equipment and access to other testing facilities. However small manufacturers can make very good speakers equipped with simpler equipment, products like MLSSA or LEAP+LMS, and their ears.

I have heard some DIY designs that are simply superb. The sound quality was by design and not an accident.

Well we may be going way :OT


I don't think there is any analytical solution (equation or otherwise) that @jinu can use


By the way, minus the fad etc., coming to technicalities, what is "sound signature"? Is this a technical term?

Years of designing amplifier drivers and I never even heard of anything like that (though I once worked with guys who were trying to do surround sound with cheap earplugs)

No it is not a technical term. Every designer has his/her own idea of what sounds 'right'. This is what makes one spreaker sound brighter than another or one speaker have tighter bass than another.

If you hear say the Vandersteen 5A it will sound very similar in timbre to the 2C or 1C. Similarly the Grand Utopia from JM-Focal will sound similar to the Diablo Utopia etc..

WinISD will do this, albeit in a slightly roundabout way. It tells you at what power level the mechanical limits of the speaker will be exceeded. Of course this depends on the box design.

Speaker Workshop, OTOH tells you exactly what the relationship between SPL/power levels are at various frequencies and you can back-calculate the power levels required depending on sensitivity. One has to keep in mind that for doubling the SPL you need ~10 times the amount of power. Usually this means immense mechanical capability in the speakers (you basically cannot run into thermal or mechanical limits at any point in normal operation), and it is not uncommon to see extreme HT setups with an array of 18" or 21" woofers.

@vina: any speaker manufacturer will make a tradeoff between on-axis and off axis response (one among many tradeoffs) based on certain assumptions about application, location, listening levels, etc. Since speakers are mechanically imperfect, any design is a mix of compromises and one has to make specific tradeoffs within a design goals and budget.

For example, some speakers may be voiced to provide the flattest possible on-axis response at the expense of narrower beam width. Yet others will optimise listening for off-axis (car speakers being a prime example) at the risk of sounding very harsh on-axis. Some design considerations are HD, resonance, efficiency, bandwidth, bass extension, power handling, speaker footprint, beam width (dispersion), budget, and mechanical and thermal limits. I may have not covered all of them. You may already know most of this given your experience. This is why different speakers actually sound different.

Really, car audio designers have the toughest time given they have absolutely no idea where the listener will be in relationship to the speakers after installation - in front, behind, above or below and by how much. The very small environment also plays a huge part in how speakers sound in cars. I guess they thank road noise, so that users do not get too critical.

Even very expensive speakers (think 30L+) have some compromises though at very high design budgets the imperfections may seem academic.

:)

Well I always thought speakers' job is to reproduce the input perfectly - the audio signal processing guys put a lot of effort into getting the timber etc. right.

If you can chracterise the frequency response and directivity of a speaker properly, and have good drivers (pretty cheap these days) then the cheapest of DSP processor can get whatever timber etc. you want via techniques like pre-distortion


I'm confused: If the impedance match is good why would doubling the SPL require 10 times the input power?

Also bigger diaphragm = better impedance matching (and conversion efficiency) at lower frequencies is what I always thought. Can you elaborate on how is it related to mechanical limits (may be via how much air it can move)


Not only the position of speakers vs. listeners, but also there are uncertainties like how will the waves flow - for example how does the roofing material behave - does it absorb, if so how much, can you get a standing wave pattern ... I didn't know that audio systems for a car can cost more than a car :D I personally wouldn't buy one if I had the money (poor ears + a background in both signal processing and analog design tells me it is a waste of money)


My point is, if you want to spend more money, speakers may be the wrong place - far better gains in acoustic quality can probably be made by things as simple as a more acoustic friendly roof lining and better seat covers.

Also while a car is, as you rightly pointed out, a very bad environment, in a way it is also a good environment if you figure out how to turn the situation into "man sitting inside a sound box"

Amplifer power:radiated sound power is a logarithmic equation. Also, the impedance of the box and speaker combo drops rapidly near box resonance, increasing the current demand from the amplifier.

Here is Linkwitz's explanation (simplified): Electrical and mechanical limits

And here is a Wikipedia type explanation. Secrets of Amplifier and Speaker Power Requirements Revealed

Basically, twice the power does not produce twice the loudness.

Twice the power will be 6dB on the sound scale. 2x here = 10x is a weird scale.

If resonance has already started, then impedance match will most likely be poor, perhaps that is why you need more power. At low amplitudes I'm certain 2x in audio requires 2x in electrical (at high amplitudes even the magnetic coil in the speaker can saturate).

by the way, if you are running near such limits, that will be a really non-linear speaker - real bad for quality performance.



thanks for the links, I'll have a look.