Bass reflex transient excursion with band-limited signal

[Circlotron]

I was thinking, if you applied a sinewave tone burst to a bass reflex sub at the port + box resonant frequency, depending on the Q of the setup, the air inside might take several cycles to get up to full amplitude at resonant frequency, and during this time the cone would have a much greater peak to peak excursion than it would at continuous tone because the air inside the box wouldn’t be loading the cone very much.

If we do a spectral analysis of an otherwise pure sinewave tone burst that starts abruptly at the zero crossing we find that there are harmonics present. But if we have, say, a 30Hz tone burst and we low pass filter it at 60Hz then we find the signal starts rather more gradually. It doesn’t get to full amplitude in the first quarter cycle but grows over several cycles.

So the question is, if running near full power, would a tone burst that is not low pass filtered be more likely to drive a woofer too far? Or would the harmonics, seeing they are of a higher frequency, simply not move the woofer cone as much anyway?

 

[bansuri]

the speaker will move identical already at the first peak, it sees the same acoustic impedance. But the sound output will be delayed by half a period.
Do not try the lower resonance without subsonic filter.

 

[chris661]

I was thinking, if you applied a sinewave tone burst to a bass reflex sub at the port + box resonant frequency, depending on the Q of the setup, the air inside might take several cycles to get up to full amplitude at resonant frequency, and during this time the cone would have a much greater peak to peak excursion than it would at continuous tone because the air inside the box wouldn’t be loading the cone very much.

I'm afraid this doesn't happen. The whole "bass reflex takes a while to come up to level" thing doesn't hold true in reality, which is this: BR is a minimum-phase system, and if you EQ it to have the same frequency response as a sealed box, the time-domain response will be identical.

I suspect that most of the bad press that BR designs receive is due to a target LF response that does not consider room gain. ie, there could be some massive LF peaking, which a sealed box (with less LF output) doesn't exacerbate as much.

If we do a spectral analysis of an otherwise pure sinewave tone burst that starts abruptly at the zero crossing we find that there are harmonics present. But if we have, say, a 30Hz tone burst and we low pass filter it at 60Hz then we find the signal starts rather more gradually. It doesn’t get to full amplitude in the first quarter cycle but grows over several cycles.

Any signal that begins abruptly has high-frequency content. Applying a low-pass filter will smooth out the abrupt change from "no signal" to "signal".

So the question is, if running near full power, would a tone burst that is not low pass filtered be more likely to drive a woofer too far? Or would the harmonics, seeing they are of a higher frequency, simply not move the woofer cone as much anyway?

It all depends on the tone burst and filtering. A tone burst with a rectangular window, for instance, will have lots of HF content. A CEA-2010 burst has almost none (because it's designed that way). Even so, the caveats you note still apply.

Chris

 

[Circlotron]

I'm afraid this doesn't happen. The whole "bass reflex takes a while to come up to level" thing doesn't hold true in reality, which is this: BR is a minimum-phase system, and if you EQ it to have the same frequency response as a sealed box, the time-domain response will be identical.

I can imagine that the sum of the cone + port output has the same overall time-domain response as a sealed box, but wouldn't that be the case simply because the (supposedly) lesser initial contribution of the port and the consequently greater initial excursion of the cone? So this doesn't actually happen in reality?

 

[TBTL]

+1 about the bursts. Certainty in time and frequency exclude each other. In other words, applying a burst that starts in a short amount of time (short time --> high certainty in time) and exciting at the port resonance frequency only (high certainty in frequency) is not possible. This is why such thought experiments are difficult to interpret accurately.

A 'sine wave' that starts not only contains harmonics, it also contains frequencies in between.


As it is possible to transform from the time domain to the frequency domain, there are different ways to look at the situation of suddenly exciting a ported speaker with a sine-shaped signal. One way is to transform the signal (simplify it to some silence followed by a sine wave) from the time domain to the frequency domain. This allow you to decompose the signal in different components, each with a different frequency. Then for each frequency, it is possible to calculate the magnitude and phase of the cone motion, specific to this frequency. Then transform back to the time domain. Sum all frequency contributions and you know the total cone motion.