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I came across this video - The Fundamentals of Sounds - where it says in 14:00:

Subwoofer is larger because it needs to be bigger for those larger low frequency waves to propagate through and the tweeter is smaller because higher frequency are very small waves and they don't need as much space to propagate

Remembering from basic physics, neither the amplitude nor the wavelength (or frequency) has anything to do with how fast a sound wave propagates. The speed of a sound wave should only be a matter of the medium, and within the same medium all sound waves should travel at the same speed. Perhaps temperature has an effect on the medium but certainly not the volume of the medium from what I recall. So the above statement does not make much sense to me.

Great if someone can help explain the physics or the concept of why a subwoofer needs to be bigger for the lower frequency waves to propagate, and vice versa for a tweeter.

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  • $\begingroup$ I thought it was just a matter of power. Lower frequencies are, well, lower. So there are fewer cycles per time interval to transfer the same amount of power. So with each cycle, you have to move a lot more energy. Holds true for electricity and EM waves too as well as far as I can tell. Also, the frequencies a membrane will resonant best at are inversely proportional to size but this again boils down to power efficiency. $\endgroup$
    – DKNguyen
    Jun 10 at 3:13
  • $\begingroup$ Your quote says nothing about the speed of sound propagation, so why do you think that the speed of sound is relevant to the production of low frequency tones? $\endgroup$
    – PM 2Ring
    Jun 10 at 8:37
  • $\begingroup$ That quote is a bit misleading or ambiguous. As one of the answers points out, impedance mismatch matters a lot. $\endgroup$ Jun 10 at 12:25
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One way to look at it is the following :

In theory, ideally, you could use one single speaker on your hi-fi, just the way it’s done on a cheap radio.

However, you would face two problems if using one single speaker instead of a medium, plus a woofer plus a tweeter:

  1. Efficiency (bandwidth):

When you send an electric signal of a given frequency f to a speaker, it will vibrate to said frequency with an amplitude $A(f)$.

An ideal speaker would have a perfectly flat frequency response, i.e. $A(f)$ would not depend much upon f:

$A(f) = Constant$

However, in practice, said response is not a flat line, but a curve, centered around a given frequency. This is due to the fact that a speaker is a physical object, with a mass, a elasticity coefficient, etc, not unlike a bell or a guitar string.

A guitar string can be modeled formally as a harmonic oscillator. When you pluck it, it yields a given note, when you shorten it by putting a finger on a fret, it will yield a more high-pitched sound and so on. Thicker strings (more massive ones) will yield lower frequencies and so on.

One could in theory build a guitar with just one thick string, however but one would face the problem that it would be inefficient at yielding high pitched tones (unless you pinch so as to shorten it dramatically) and conversely, if it is a rather lightweight one, one would have to build a really ridiculously long guitar to yield the low notes.

The efficient solution for a guitar is to have a set of different strings, with different tensions and different masses.

For analogous reasons, a speaker with a certain mass, diameter, elasticity will be able to reproduce efficiently sound, as a (frequency dependent) response to the electrical signal which is send to it, in a limited frequency range.

Therefore to reproduce efficiently the whole spectrum of sound covering the range of human hearing, one uses a set of two or three or more loudspeakers whose natural frequency response curves overlap, so as to complement each other and cover the whole required range.

  1. Quality.

Just as when attempting to use a single guitar string to cover the whole range of the guitar (say: just using the low E string and pinch it really high to reach high pitched notes), one would face a quality problem on top of the aforementioned efficiency problem (very high pitched notes on a thick E string would be hard to distinguish), reproducing frequencies well beyond the efficient part of the frequency response of a speaker would not only require more energy, but it would not yield the same définition/clarity as adding a supplementary dedicated speaker (for a given frequency range).

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subwoofers need to be bigger than tweeters because as the frequency is reduced, the radiation resistance of the speaker cone goes down because the cone impedance is mismatched relative to the air it is radiating into. To remedy this, the cone diameter needs to be increased for best efficiency at low frequencies.

This "best diameter" scales more or less linearly with frequency, so a 1" tweeter that radiates well at 10,000 Hz gets scaled up to 12" to radiate well at around 800 Hz. A problem arises when you want to radiate efficiently at 100 Hz because that implies a 10 foot diameter cone. So instead, the cone excursion is increased which allows 15" and 18" cones to radiate well below 100 Hz. Those cones move back and forth as much as 1" total, a job which requires hundreds of watts RMS of electrical power to perform.

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