Driver behaviour w.r.t. frequency/power

[454Casull]

Let's say I have a electrodynamic multi-driver loudspeaker with a flat on-axis response and constant directivity index. This loudspeaker has a filter module with a HP at 20 Hz and a LP at 20 kHz; both are 4th-order LR.

1) Given x number of drivers, at (x-1) crossover points at Fx1, Fx2... F(x-1), with Sd1, Sd2... Sdx, what would be the peak diaphragm excursion experienced by each driver in order to achieve a measured 110 dB system SPL at 1 m with Gaussian white noise input?

2) Given 1), and the power sensitivity of each driver (assume active amplification), what would be the necessary power input to each driver in order to achieve a measured 110 dB system SPL at 1 m with Gaussian white noise input?

3) Given x number of drivers, at (x-1) crossover points at Fx1, Fx2... F(x-1), with Sd1, Sd2... Sdx, and an arbitrary power distribution vs. frequency function*, what would be the peak diaphragm excursion experienced by each driver in order to achieve a measured 110 dB SPL at 1 m with white noise input enveloped by the power function?

4) Given 3), and the power sensitivity of each driver (assume active amplification), what would be the necessary power input to each driver in order to achieve a measured 110 dB SPL at 1 m with white noise input enveloped by the power function?

*See Figure 1 here: Why Do Tweeters Blow When Amplifiers Distort?

[454Casull]

I will upload a spreadsheet in a few hours which may help to assemble your thoughts.

[whgeiger]

VD capacity of a driver limits the lowest frequency to be passed to it for a given output level. That sets the high pass filter frequency and slope which intern forms the basis for sizing the amplifier to drive it according to its efficiency. Your question looks like a homework assignment from a loudspeaker design or similar course and bears a degree of complexity greater than that needed to solve the underlying problem of driver and power amplifier selection and sizing in a setting of an active crossover and dedicated power amplifiers. Simply start at the lowest high-pass filter frequency and work forward to the highest.
See this thread for some details
SPL vs. Frequency vs driver movement
Regards,

WHG

[454Casull]

Originally Posted by whgeiger

VD capacity of a driver limits the lowest frequency to be passed to it for a given output level. That sets the high pass filter frequency and slope which intern forms the basis for sizing the amplifier to drive it according to its efficiency. Your question looks like a homework assignment from a loudspeaker design or similar course and bears a degree of complexity greater than that needed to solve the underlying problem of driver and power amplifier selection and sizing in a setting of an active crossover and dedicated power amplifiers. Simply start at the lowest high-pass filter frequency and work forward to the highest.
See this thread for some details
SPL vs. Frequency vs driver movement
Regards,

WHG

You will note that I actually posted in that thread.

Yes, if you want to approximate and go by "rule of thumb" then all of this is not necessary. But there is currently no maths, so far as I can tell, that will help somebody understand what is going on to a exact level. By the way these are not homework questions - I developed them myself while creating the thread.

For example, what is the change in power requirements for each driver going from a 2-way to 5-way?

Another example - how do you calculate the peak excursion of a woofer which is used to reproduce 300 Hz to 2 kHz, given a target system SPL measured while playing "music" (hence "arbitrary power distribution function")? It doesn't make any sense to say that since a system needs to do 120 dB at 1m, the woofer needs to be capable of doing a sine wave at its high-pass corner frequency at 120 dB (whose required Xmax can easily be calculated given the Sd)... unless the system is expected to also be able to play single tones at same peak output - these tones are impossible in nature, anyway. So how exactly does the woofer's output measure when playing in the system, and what does the excursion vs time function REALLY look like?

[whgeiger]

Peak driver excursion will occur at the lowest frequency of its pass-band, irrespective of whether the signal is component of Gaussian white noise or not. That is acoustical fact not some mindless "rule of thumb". The output limit on the entire system will be set by this condition. The question remains, in which pass-band it will occur first? The math tools to determine this exist. Solution to your problem would be for this to occur at equal levels in each channel at a magnitude somewhere above 110 db SPL @ 1 meter in front of each driver.

Regards,

WHG

[454Casull]

Originally Posted by whgeiger

Peak driver excursion will occur at the lowest frequency of its pass-band, irrespective of whether the signal is component of Gaussian white noise or not.

Regards,

WHG

I don't doubt that (well, maybe for infra-bass). But, what is the peak driver excursion (quantity-wise)?

[Ron E]

Idea for you. Get audacity, make a white signal, chop it up into bands and play with the spectrum analyzer. Either that or get a book on college level acoustics. This is an involved question, and I think there is more to it perhaps than you are posting - often the motivation is as fundamental as the question.

Pink noise is probably a better model signal for music - but even that has too much high frequencies.

[454Casull]

Originally Posted by Ron E

Idea for you. Get audacity, make a white signal, chop it up into bands and play with the spectrum analyzer. Either that or get a book on college level acoustics. This is an involved question, and I think there is more to it perhaps than you are posting - often the motivation is as fundamental as the question.

Pink noise is probably a better model signal for music - but even that has too much high frequencies.

That's a good idea.

Yes, even pink noise has too much treble... hence the questions involving the power distribution curves.

[454Casull]

attached

[whgeiger]

Originally Posted by 454Casull

I don't doubt that (well, maybe for infra-bass). But, what is the peak driver excursion (quantity-wise)?

The information you require may be found in the section entitled Large Signal Performance starting on AESJ Pg. 279

http://diyaudioprojects.com/Technica...m-Analysis.pdf

Regards,
WHG