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?
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?
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.
454Casull said:
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.
Is the total SPL based on the total excursion, then?
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?
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?
The displacement plot, that people compare to Xmax, is a result in the frequency domain. If you have the phase components that go with the displacements, all you have to do is take the inverse FFT to get a time trace which is the time domain impulse displacement response. Then look at the peak dispacement and ring out in the time domain and see how it is compares with the original displacement plot in the frequency domain to get a feel for how much motion a pulsing music-like signal might produce.
Personally, I do not put much emphasis on displacement plots in the frequency domain. I believe that conclusions drawn from these types of plots concerning how much power a driver can handle before it exceeds Xmax are way too comservative. I have observed that a driver typically does not move as much as this plot would indicate when music is being played even at high volume levels. Maybe Home Theater and sound effect records are different, but for acoustic music I don't worry as much as some people about driver displacement.
Personally, I do not put much emphasis on displacement plots in the frequency domain. I believe that conclusions drawn from these types of plots concerning how much power a driver can handle before it exceeds Xmax are way too comservative. I have observed that a driver typically does not move as much as this plot would indicate when music is being played even at high volume levels. Maybe Home Theater and sound effect records are different, but for acoustic music I don't worry as much as some people about driver displacement.
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