SPL and excursion

454Casull · 19th April 2009, 12:53 AM

I have no idea how to solve this sort of problem, so I'm falling back on you guys. This is not homework, by the way.

An acoustically-small driver that fires into half-space plays a full-spectrum sound (that is, equal energy at all frequencies between 20 Hz and 20 kHz) but is 4th-order L-R bandpassed at 150 Hz and 600 Hz. The C-weighted (flat) SPL at 1 m is measured to be 110 dB. What is the peak-to-peak excursion of the driver?

Brett · 19th April 2009, 04:49 AM

Model the particular driver in Unibox and look at the Xcurs curve.

Here is a curve for the required volume displacement for a given spl and freq. Extrapolate to fit your requirements.

454Casull · 19th April 2009, 05:24 AM

I can do that with either WinISD or SL's spl_max spreadsheet, but AFAIK the numbers are only valid for single tones. Any given SPL that is comprised of various frequencies should have less amplitude per freq, right?

Brett · 19th April 2009, 06:07 AM

Quote:

Originally posted by 454Casull
I can do that with either WinISD or SL's spl_max spreadsheet, but AFAIK the numbers are only valid for single tones. Any given SPL that is comprised of various frequencies should have less amplitude per freq, right?

Did you bother to look at and think about the above graph?
For a given SPL the LF requirements dominate xcurs.

454Casull · 19th April 2009, 06:39 AM

Quote:

Originally posted by Brett
Did you bother to look at and think about the above graph?
For a given SPL the LF requirements dominate xcurs.

Fine. What is the error of the calculated excursion when assuming a single tone at the lowest reproduced frequency? At what low-pass point does this error become excessive?

Brett · 19th April 2009, 08:58 AM

What the graph shows is the calculated amount (volume) of air needed to be displaced at a given frequency to produce a certain SPL. HOW you do that is irrelevant. How much error between a measured result for a given driver and the calculated will depend upon the driver and it's linearity. That you need to MEASURE.

Ron E · 19th April 2009, 01:29 PM

Quote:

Originally posted by 454Casull
I can do that with either WinISD or SL's spl_max spreadsheet, but AFAIK the numbers are only valid for single tones. Any given SPL that is comprised of various frequencies should have less amplitude per freq, right?

Modeling the loudspeaker as a linear system, superposition holds.
The excursion is the vector sum of the excursions at each frequency. I know of no analytic expression for noise, or music, so you will have to approximate it by brute force.

You could start at 20Hz and go up at 1/12 octave intervals.

454Casull · 19th April 2009, 09:50 PM

Quote:

Originally posted by Brett
What the graph shows is the calculated amount (volume) of air needed to be displaced at a given frequency to produce a certain SPL. HOW you do that is irrelevant. How much error between a measured result for a given driver and the calculated will depend upon the driver and it's linearity. That you need to MEASURE.

Sorry, I believe you misunderstand me.

Quote:

Originally posted by Ron E

Modeling the loudspeaker as a linear system, superposition holds.
The excursion is the vector sum of the excursions at each frequency. I know of no analytic expression for noise, or music, so you will have to approximate it by brute force.

You could start at 20Hz and go up at 1/12 octave intervals.

Thanks, Ron. Too bad, eh?

Is the total SPL based on the total excursion, then?

Ron E · 19th April 2009, 11:25 PM

Don't get me wrong, There are a number of ways to approximate this.

The simplest is to calculate the excursion at each frequency and add them up.

The excursion at F1 = X1
Excursion at time t, due to F1 = X1*sin(2*pi*F1*t)
Do this for every frequency...This is brute force.

You could also generate a model and apply a stimulus.

For your example, you have the added complexity of a bandpass filter.
I could do this, but not for free, what is it worth to you to know the answer?

454Casull · 19th April 2009, 11:37 PM

Quote:

Originally posted by Ron E
Don't get me wrong, There are a number of ways to approximate this.

The simplest is to calculate the excursion at each frequency and add them up.

The excursion at F1 = X1
Excursion at time t, due to F1 = X1*sin(2*pi*F1*t)
Do this for every frequency...This is brute force.

Do I sum the SPLs from each frequency individually, then?

Quote:

Originally posted by Ron E
I could do this, but not for free, what is it worth to you to know the answer?

Right now? Absolutely nothing.

19th April 2009, 12:53 AM	#1
454Casull diyAudio Member Join Date: Jan 2004 Location: Toronto, ON, Canada	SPL and excursion I have no idea how to solve this sort of problem, so I'm falling back on you guys. This is not homework, by the way. An acoustically-small driver that fires into half-space plays a full-spectrum sound (that is, equal energy at all frequencies between 20 Hz and 20 kHz) but is 4th-order L-R bandpassed at 150 Hz and 600 Hz. The C-weighted (flat) SPL at 1 m is measured to be 110 dB. What is the peak-to-peak excursion of the driver? __________________ Building a 2.1 system out of a 3/4"x4'x8' sheet

19th April 2009, 05:24 AM	#3
454Casull diyAudio Member Join Date: Jan 2004 Location: Toronto, ON, Canada	I can do that with either WinISD or SL's spl_max spreadsheet, but AFAIK the numbers are only valid for single tones. Any given SPL that is comprised of various frequencies should have less amplitude per freq, right? __________________ Building a 2.1 system out of a 3/4"x4'x8' sheet

19th April 2009, 11:25 PM	#9
Ron E diyAudio Member Join Date: Jun 2002 Location: USA, MN	Don't get me wrong, There are a number of ways to approximate this. The simplest is to calculate the excursion at each frequency and add them up. The excursion at F1 = X1 Excursion at time t, due to F1 = X1sin(2piF1t) Do this for every frequency...This is brute force. You could also generate a model and apply a stimulus. For your example, you have the added complexity of a bandpass filter. I could do this, but not for free, what is it worth to you to know the answer? __________________ Our species needs, and deserves, a citizenry with minds wide awake and a basic understanding of how the world works. --Carl Sagan Science is a way of thinking much more than it is a body of knowledge. --Carl Sagan

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19th April 2009, 08:58 AM	#6
Brett diyAudio Member Join Date: Jan 2002	What the graph shows is the calculated amount (volume) of air needed to be displaced at a given frequency to produce a certain SPL. HOW you do that is irrelevant. How much error between a measured result for a given driver and the calculated will depend upon the driver and it's linearity. That you need to MEASURE.

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