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I was watching this video. The experiment is to create a square signal and record what is outputted by a speaker. We see two diracs signal (+ and -) that looks like the derivative of the signal. Can anyone explain this phenomena? My intuition is that it is caused by some really high frequencies that are out of range for the speakers designed for human. But why the derivative?

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    $\begingroup$ "We see two diracs signal" Sorry to be nerdy, but no we don't. The Dirac delta functional is not an actual function, nor is it physically possible. Reality would break. You're seeing two pronounced spikes. Granted, I know what you mean -- but don't be mislead into thinking that the Dirac delta function can ever be a physical phenomenon. It's a handy mathematical tool, nothing more. $\endgroup$ – TimWescott Jul 10 at 15:03
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Imagine an amplifier/speaker combination with no DC blocking, so the speaker cone moves exactly in proportion to the input voltage.

Now imagine a microphone that measures the actual absolute pressure of the atmosphere, again with no DC blocking.

Even with such a speaker and microphone, because of the finite size of the speaker, the air will act as a highpass filter.

It's complicated, and I'd have to do some research myself to be able to put numbers to it, but roughly speaking the actual response of the sound pressure to the speaker position is going to start rolling off at about the point where the wavelength is the same order of magnitude as the speaker's diameter. There will be much better information out there on the web, but I suspect you can search it as well as I can.

This is why woofers are bigger than tweeters, and its why subwoofers are constructed so (seemingly) oddly. Subwoofers, in particular, are significantly smaller than a wavelength of the sound they're producing, so the designers need to play all sorts of acoustic tricks to make them work, and they're horribly inefficient, which is why they often need -- or come with -- their own amplifiers.

When the speaker pushes out suddenly in response to the square wave, it tries to generate a permanent rise in pressure -- but for wavelengths longer than the box, the pressure wave more or less goes around the box and into the hole in the back, and very little sound is produced. What's left is that spike you see.

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  • $\begingroup$ As I pointed out to Olli in a different question. Coupling capacitors play a huge role here. $\endgroup$ – Cedron Dawg Jul 10 at 15:18
  • $\begingroup$ @Cedron Dawg, do they? I don’t see how. They would have some effect on the frequency response, but hopefully it wouldn’t be noticeable. They’d be included to prevent low frequency current from going through the speaker, which could result in distortion or damage, but it shouldn’t have a drastic effect on the acoustics. $\endgroup$ – Dan Szabo Jul 10 at 15:32
  • $\begingroup$ @DanSzabo They function as a high pass filter. In the audible range, they shouldn't have any effect (ideally), however, the example here and in the other question is about passing a DC signal. A coupling capacitor can hold a DC difference all day long and happily pass any ripples through. Handy when you have a biased current in a class A amplifier, yes? $\endgroup$ – Cedron Dawg Jul 10 at 15:47
  • $\begingroup$ @Cedron Dawg, oh for sure. They’d arguably be more handy than the heat sink for a unipolar class A amp. What I was getting at was that given the set up of a speaker driven with a test waveform and a measured response on a microphone, the response would be high pass filtered regardless of whether or not coupling capacitors were used. The presumed air volume of the room would be too high for the deflection of the speaker to matter, and the microphone wouldn’t pick it up even if it did. $\endgroup$ – Dan Szabo Jul 10 at 15:59
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    $\begingroup$ That's the point I'm trying to make -- even with no high-pass filtering in the electronics, the response from the speaker to the mic will still be high-passed just because of the physics of sound. $\endgroup$ – TimWescott Jul 10 at 19:53
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A speaker does not have the ability to produce DC frequencies, at least not in any practical way. As such, the frequency response would include a zero at zero Hz, which corresponds to a high pass filter. A derivative is a type of high pass filter, which would explain why it looks a bit like the derivative. Real speaker responses have a fair bit of complexity, but generally approach zero at low frequencies and high frequencies, so at a macro scale are more like band pass filters. The actual frequency response is a function of the electromechanical characteristics of the system.

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