Physics...why small speakers can't reproduce low frequencies

[Sylar]

I was reading about speakers, bass related stuff (Bass Management Basics – Settings Made Simple) at the AV University. Just started my graduation.

Had a couple of questions as to how how & why things work this way.
Why is it that small diameter speakers cant faithfully reproduce low frequency signals? With a larger speakers & larger diameter, the surface area is more, and more air is pushed around to create sound. Also larger speaker cones move further to & fro, compared to smaller, right?
So what is it about LF, that requires more air to be pushed to create the LF sounds?

 

[highfigh]

I was reading about speakers, bass related stuff (Bass Management Basics – Settings Made Simple) at the AV University. Just started my graduation.

Had a couple of questions as to how how & why things work this way.
Why is it that small diameter speakers cant faithfully reproduce low frequency signals? With a larger speakers & larger diameter, the surface area is more, and more air is pushed around to create sound. Also larger speaker cones move further to & fro, compared to smaller, right?
So what is it about LF, that requires more air to be pushed to create the LF sounds?

If you think of low frequencies as somewhat omni-directional, it means that, for a given SPL, a lower percentage of the energy produced by the speaker reaches the listener's ears than directional sound. If the sound from a directional speaker is like a cone, the sound from bass frequencies that are basically omni-directional are like a sphere. Sound is energy and if there's to be any hope of the listener hearing the low frequencies, the cone area must be larger in order to produce enough energy to match the SPL of the mid and tweeter. For a given amount of cone excursion, a small driver moves far less air and that's the main reason small speakers don't produce as much bass but some small drivers can have pretty large excursion. Some of the energy going behind the speaker can be regained by placing the speaker near at least one boundary and if possible, two or three.

 

[XEagleDriver]

Why is it that small diameter speakers cant faithfully reproduce low frequency signals?

Small speakers can faithfully reproduce low frequency signals, but at very soft (i.e. quiet) volume levels which are only useful at very close distances. This is what allows ear buds and headphones to reproduce reasonable bass!

So what is it about LF, that requires more air to be pushed to create the LF sounds?

It does NOT require more air to be pushed to create a LF sound (i.e. a low frequency), but it DOES to create it at an amplitude (i.e. loudness) large enough to be useful at typical listening distances.

With my apologies to real physics folks, a useful way to think of it is as follows:
Picture one tuning fork vibrating at both 30Hz and then at 3000Hz. Furthermore, each tuning fork is displacing back and forth from its at center rest position the same distance (i.e. amplitude).

The fork imparts energy to the air around it with each to-n-fro motion, so the 3000 Hz frequency is imparting 100 times the energy to the air around it compared to the 30 Hz frequency, because it is moving to-n-fro the same distance more often.

The way to compensate for this difference in energy transfer is to make the "30 Hz" tuning fork have a larger surface area, and/or move back-n-forth a longer distance to mitigate this 100 fold difference! (A lot like woofers - i.e. larger surface areas and a longer throws than mid or tweeter speakers)

Or in physics lingo "Sound Intensity = Energy / Time * Area" so to achieve the same sound intensity (SPL or dB to you an I) if the Energy/Time is low (i.e. 30 Hz) then we must increase the area (woofer size and movement) to compensate.

With a larger speakers & larger diameter, the surface area is more, and more air is pushed around to create sound.

Not necessarily, it depends on the amplitude of the speaker movement (to-n-fro distance the speaker moves). Or another way, picture the gentile wiggle of the speaker cone to make a soft low frequency sound versus the large throw to make a LOUD low frequency sound.

Larger speaker cones move further to & fro, compared to smaller, right?

Not necessarily again. Larger speakers (i.e. woofers) are typically designed to move further to-n-fro for the reasons we discussed above, but they do not HAVE to move far if the desired sound intensity is soft (i.e. quiet).

Hope that did not muddy the water to much.

If not, check out: this or this

Cheers,
XEagleDriver

 

[FirstReflection]

Just to build upon XEagleDriver's nice explanation:

here is a rough analogy that is easy to picture and helps you to understand what is going on

As XEagleDriver pointed out, it is all about amplitude.

Picture a small cork floating in a still pool of water. You can push down on that cork and allow it to pop back up. If you push it down and let it pop back up with a steady, even rhythm, you'll create a nice wave along the water's surface.

Now, if we want to make waves in the water that sort of resemble sound waves, then they have to be nice and smooth and even with that perfect sin wave shape that you would see on an oscilloscope. In order to create those kinds of waves by pushing down on our small cork and letting it pop back up, we cannot push it below the surface of the water, nor can we allow it to "jump" above the surface of the water. That would create weird, uneven ripples and wouldn't let us produce that nice, even sin wave shape. Also, the up and down motion would have to be nice and steady. You couldn't push it down quickly, hold it down and then let it pop back up. That would create "gaps" in the wave and wouldn't create that nice, even sin wave shape.

So even just picturing that in your mind, it's rather easy to picture that if you're pushing the small cork down and letting it pop back up at quite a fast rate (high frequency), you can create waves that are fairly tall. The height of the waves is the amplitude - and if they were sound waves, that would be the "loudness" of the sound.

It's also easy to picture that if you push that cork down slowly and let it pop back up slowly (a low frequency), you're going to create very shallow waves that have very little height (amplitude).

Now, if we replace the small cork with a big disc, again, it's pretty easy to picture what happens. With that large surface area being able to displace so much more water than the small cork, we can also create taller waves at lower frequencies.

This analogy also makes it easy to understand some other concepts. For example, it's fairly easy to picture that you could create the same height waves using something with the diameter of the small cork rather than the big disc, but that smaller diameter device would have to be much, much taller so that you could push it much deeper into the water in order to create the same height in the waves. This helps you to picture the concept of driver excursion in a speaker. You could play loud (high amplitude), low frequency notes with a small driver (like a tweeter), but it would have to move really far out and really far back in - it would have to have HUGE excursion. So it is much, much, much more efficient to use a big disc in the water or a speaker driver that has a much larger diameter. It can create higher amplitude, low frequency waves without needing the same massive excursion as a small diameter driver.

On the other end of the spectrum, if you're pushing down on that big disc in the water with your finger, it's pretty easy to push it down and have it pop back up at a nice, slow rhythm. But try to move it really quickly and it gets tough. All of that big surface area doesn't easily move up and down quickly. It's much easier to bob that small cork up and down at a fast rate vs the big disc.

In the end, if the idea is to create waves of the same height (amplitude) regardless of the frequency, then it just makes sense to use a small diameter device for the high frequencies and a large diameter device for the low frequencies. Either diameter can do the entire job, but it becomes inefficient. The small diameter driver has to move extremely far in order to create the low frequencies (at the same amplitude as the high frequencies) and the big disc is difficult to move quickly, but rather easy to move at slow, low frequencies.

This is by no means a proper scientific explanation! But it's just an easy way to sort of picture what is going on and get a grasp on why speakers use small tweeters for the high frequencies and large drivers for the low frequencies

 

[nauc]

simple...

a speaker must move 2x as much every time you go down an octave to produce the same amount of volume and since that would require the speaker to move A LOT, to keep up with the "mains", its easier to create a speaker that has a big diameter, that doesnt have to move as much

 

[GO-NAD!]

Just to build upon XEagleDriver's nice explanation:

here is a rough analogy that is easy to picture and helps you to understand what is going on

As XEagleDriver pointed out, it is all about amplitude.

Picture a small cork floating in a still pool of water. You can push down on that cork and allow it to pop back up. If you push it down and let it pop back up with a steady, even rhythm, you'll create a nice wave along the water's surface.

Now, if we want to make waves in the water that sort of resemble sound waves, then they have to be nice and smooth and even with that perfect sin wave shape that you would see on an oscilloscope. In order to create those kinds of waves by pushing down on our small cork and letting it pop back up, we cannot push it below the surface of the water, nor can we allow it to "jump" above the surface of the water. That would create weird, uneven ripples and wouldn't let us produce that nice, even sin wave shape. Also, the up and down motion would have to be nice and steady. You couldn't push it down quickly, hold it down and then let it pop back up. That would create "gaps" in the wave and wouldn't create that nice, even sin wave shape.

So even just picturing that in your mind, it's rather easy to picture that if you're pushing the small cork down and letting it pop back up at quite a fast rate (high frequency), you can create waves that are fairly tall. The height of the waves is the amplitude - and if they were sound waves, that would be the "loudness" of the sound.

It's also easy to picture that if you push that cork down slowly and let it pop back up slowly (a low frequency), you're going to create very shallow waves that have very little height (amplitude).

Now, if we replace the small cork with a big disc, again, it's pretty easy to picture what happens. With that large surface area being able to displace so much more water than the small cork, we can also create taller waves at lower frequencies.

This analogy also makes it easy to understand some other concepts. For example, it's fairly easy to picture that you could create the same height waves using something with the diameter of the small cork rather than the big disc, but that smaller diameter device would have to be much, much taller so that you could push it much deeper into the water in order to create the same height in the waves. This helps you to picture the concept of driver excursion in a speaker. You could play loud (high amplitude), low frequency notes with a small driver (like a tweeter), but it would have to move really far out and really far back in - it would have to have HUGE excursion. So it is much, much, much more efficient to use a big disc in the water or a speaker driver that has a much larger diameter. It can create higher amplitude, low frequency waves without needing the same massive excursion as a small diameter driver.

On the other end of the spectrum, if you're pushing down on that big disc in the water with your finger, it's pretty easy to push it down and have it pop back up at a nice, slow rhythm. But try to move it really quickly and it gets tough. All of that big surface area doesn't easily move up and down quickly. It's much easier to bob that small cork up and down at a fast rate vs the big disc.

In the end, if the idea is to create waves of the same height (amplitude) regardless of the frequency, then it just makes sense to use a small diameter device for the high frequencies and a large diameter device for the low frequencies. Either diameter can do the entire job, but it becomes inefficient. The small diameter driver has to move extremely far in order to create the low frequencies (at the same amplitude as the high frequencies) and the big disc is difficult to move quickly, but rather easy to move at slow, low frequencies.

This is by no means a proper scientific explanation! But it's just an easy way to sort of picture what is going on and get a grasp on why speakers use small tweeters for the high frequencies and large drivers for the low frequencies

I like that analogy!