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101 sound question: bass from a small speaker or how high is that wave?

I don't understand some of the basics of sound but i want to learn. My question of the day is: How can headphones generate bass with small drivers?

I get it that a 20hz tone is 56.5 ft long (1130 ft./sec.(speed of sound)  and divide it by 20), but what makes it "deep?" Is it the length, height or width of the waves?  It would seem to be the height of the waves given that bass drivers in speakers are bigger than tweeters, but then how can bass waves come from a headphone driver? I've never seen (and never will see) a bass driver in a speaker that is the size of my ear.

*cocks his head*
Music lover and recovering high end audiophile

Re: 101 sound question: bass from a small speaker or how high is that wave?

Reply #1
I get it that a 20hz tone is 56.5 ft long (1130 ft./sec.(speed of sound)  and divide it by 20), but what makes it "deep?"

what?

Re: 101 sound question: bass from a small speaker or how high is that wave?

Reply #2
I get it that a 20hz tone is 56.5 ft long (1130 ft./sec.(speed of sound)  and divide it by 20), but what makes it "deep?"
High tones come from tweeters (small drivers). Low tones come from woofers (big drivers).  How can you get a low tone from a small driver, and does the length, width or height of the wave determine the frequency of the tone? Or is it the speed (hence the word frequency), or all of it?

what?
Music lover and recovering high end audiophile

Re: 101 sound question: bass from a small speaker or how high is that wave?

Reply #3
How can you get a low tone from a small driver, and does the length, width or height of the wave determine the frequency of the tone?

The length, width and height of a wave are determined by the volume of the space you play it in (unless you mean wavelength, which is just the inverse of frequency).  With a speaker, that is the size of the room you are in.  They are not related to frequency. 

For a pair of headphones it won't matter that the driver is very small because it is very close to your ear and you don't need to generate a lot of acoustical power at short distances. 

Re: 101 sound question: bass from a small speaker or how high is that wave?

Reply #4
> what makes it "deep?"
The frequency, and since sound's speed is constant, that's equivalent to the length, i.e. the wavelength.

Sound waves don't really have an intrinsic height of width, although they can be constrained by a room. They're longitudinal pressure waves, meaning the variation is backwards and forwards moving molecules as it propagates. The sine wave you see in images and audio applications is not the sound. It's the graph of the pressure as it passes a certain point (this is why it's extra funny/tiresome when antidigitalists talk about stair-stepped sound).

There are tweeters and woofers of different sizes because it's easier to get certain frequencies out of certain sized objects at a significant intensity.

Re: 101 sound question: bass from a small speaker or how high is that wave?

Reply #5
An ideal speaker can play any frequency on the same level without distortion. But unfortunately, that speaker does not exist. Every speaker has physical limitations. The closer to the ideal speaker, the better it sounds.

Human ear is not linear hearing. It is less sensitive to bass frequency than to the midrange. To hear them equally loud, the bass tone must be much stronger (higher amplitude), so more power is needed to reproduce it.

The louder a tone,  the more air must be moved.

You have two options to give a loudspeaker the ability to "move enough air": A bigger cone or let it swing stronger.
The first choice is the one with fewer downsides so it is used in most of speakers. That is, why woofers are so big in contrast to the tweeters. The tweeter is needed because the bigger cone isn't fast enough to be able to reproduce high frequency.

A headphone is much closer to the ear and the room between speaker and ear is sealed so there is much less loss. It does not need much power to be damn loud. The speaker itself is big enough to "move enough air" (lesser needed because the distance is much smaller and the room between speaker and eardrum is sealed) and even small enough to reproduce high frequency.

If you take  the head phone off while it is playing, then the seal breaks and the bass suddenly drops and you hear just treble. Like a regular loudspeaker without woofer.

And there are high-quality widerange speakers that plays all frequencies trough one single cone. That cone is a very good midrange speaker with ability to reproduce bass and treble too. These speakers are closest to the "ideal speaker" so the overall sound quality is usually very good. But there are weaknesses in very high and very low frequencies, since it does not move enough air for the lowest frequencies, and it is too sluggish to follow the highest frequencies.

Re: 101 sound question: bass from a small speaker or how high is that wave?

Reply #6
Perhaps one of the bad things about trying to get a lot of wide freq range sound amplitude out of single cone speakers is that the wide excursion required for the low frequencies (at high amplitude) modulates the high frequencies.  This causes a kind of doppler distortion -- intermodulation.   It is very difficult for a single diaphragm to reproduce wide freq range at very high signal levels with the best quality.   For small signal levels -- it works very well.

Re: 101 sound question: bass from a small speaker or how high is that wave?

Reply #7
Quote
I don't understand some of the basics of sound but i want to learn. My question of the day is: How can headphones generate bass with small drivers?
It's close to your ear...    If it can move back-and-forth at 20Hz (20 cycles per second) and if it's close-enough to move your eardrum back-and-forth at 20Hz, you're good to go!

My physics is rusty, but I believe it takes a big woofer get good bass (in a room) because it's moving more slowly and to get the same amount energy as higher frequencies, you've got to move more air. 

And, our ears are less sensitive to bass so it just takes more energy.    (Our hearing is less sensitive to the highest frequencies too, but it's "worse" at the lowest frequencies.)

Re: 101 sound question: bass from a small speaker or how high is that wave?

Reply #8
Quote
I don't understand some of the basics of sound but i want to learn. My question of the day is: How can headphones generate bass with small drivers?
It's close to your ear...    If it can move back-and-forth at 20Hz (20 cycles per second) and if it's close-enough to move your eardrum back-and-forth at 20Hz, you're good to go!

My physics is rusty, but I believe it takes a big woofer get good bass (in a room) because it's moving more slowly and to get the same amount energy as higher frequencies, you've got to move more air. 

And, our ears are less sensitive to bass so it just takes more energy.    (Our hearing is less sensitive to the highest frequencies too, but it's "worse" at the lowest frequencies.)

You are right about the big woofer moving more air -- necessary to send the LF through the air.  However, that woofer by itself usually has two sides -- the front and back.   The back has 180deg phase shift from the front, except for the phase shift due to the distance/wavelength (which is fairly long for LF audio), so the distance between back and front is very LOW in terms of degrees.  This means that the cancellation (addition of signal + signal@180degrees is zero) is very significant.   This is why a big woofer by itself in the middle of the room isn't very loud.  You can either block the back from the front (e.g. air suspension or infinite baffle), or phase shift the rear and wrap the rear signal to the front using some kind of duct scheme.   Theoretically, the phase shift approach can be approx twice as efficient as the rear blocking mechanisms -- but the phase shift approach requires lots of math to do correctly. 

You can do the experiment yourself.   Take a big woofer,  suspended in the middle of a room, and apply a bass tone.   That bass tone will be fairly weak.   Then, take that same woofer, but place it on a large rectangular baffle (basically the front part of a speaker system) -- make sure the baffle is at least 3-4' by 3-4'.   You'll notice that there is much more audible bass.  If you further take a perhaps smaller baffle --- but very solid, and make it the front of a speaker box.   Seal that speaker box as tightly as you can (very little, minimum necessary air flow), you notice significantly more bass yet.
In the case of headphones, it is easy to closely couple the diaphragm to the ear -- of course, the freq resp of the headphone must take the leakage from back to front even in that case (but is not quite so severe because of the nearer field coupling to the ear.)

Way back in the day, the air suspension (or acoustic suspension) speakers were a godsend -- amplifier power became easier and easier to come by, so the loss of power to warming the air in the box wasn't so significant.  Then, we could have lots of bass with a small box.   You could really feel the vibration on those small boxes, and any loss of glue could cause nasty sounding vibrations.

John

Re: 101 sound question: bass from a small speaker or how high is that wave?

Reply #9
Quote
that woofer by itself usually has two sides -- the front and back.   The back has 180deg phase shift from the front...
We're getting off-topic, but yes that's why speakers are in a box.  ;)  

...A headphone can be open in the back and as long as it's sealed (or "partially sealed") around the ear, the out-of-phase soundwaves can't come-around to the front.   ...Or, you could mount a woofer in a wall between two rooms and you'd get bass in both rooms.

Re: 101 sound question: bass from a small speaker or how high is that wave?

Reply #10
There are actually three approaches -- two might be partially related, but are somewhat different in important ways.  Those differences ARE useful for headphones.  When you mentioned headphones -- I started looking at the differences in coupling between speakers and headphones -- and noted your explanation and recognized that we had been a little 'uncareful' talking about headphones and too easily implying too much similarity between the use/situation where headphones are used vs. speakers.   A significant amount of that 'uncarefulness' had been my fault.  There are also nearfield/coupling differences for different kinds of speakers (e.g. studio monitors)  headphones use nearfield also along with some isolation (depending on design.)   Open air headphones work without explicit isolation, there is a closer coupling to the ear -- it isn't because of explicit isolation.

Actually, it all seems to be important as to  how to get bass to appear and work correctly.   Again to explain how long wavelengths have to be dealt with -- there are several major approaches (and one minor approach often used on headphones & less-so studio monitors.) we did describe one ot the 'isolating' or coupling approach -- which is to isolate the rear from the front or direct coupling.  However, there is also an approach VERY often used back in the day when power amplifier design was challenged to output more than several 10s of watts -- reflex type speakers.   Reflex designs are not usually needed for headphones, because of both the natural isolation, but MORE IMPORTANTLY -- the use of near field to couple to the ear.  Reflex designs do an explicit 180degree phase reversal from the rear -- at least, ideally.  So, that power that would have been lost by the 'isolation' method is not lost.   Back in the old days, when a 20-60watt amplifier was a space heater, a bass reflex (or even horn) design was a very good choice.

Headphones don't just use the isolation method alone (which I am afraid was previously implied), but also there is a nature of waves where near field more direct coupling works differently and perhaps more efficiently.   This is akin to using near-field in RF, where one gets tighter coupling and even mutual interference between the transmitter & receiver (in near field.)  I believe that headphones also take advantage of that -- so that the rear side isn't really directly isolated, but instead the shape of the transducer along with the wavelength cause better coupling.  So, the differing pressure and coupling to the ear also have an effect.  SO, for headphones and isolating forms of speakers, those are kind of mode 1A and 1B (rather than being the same, or being totally different.)  The reflex designs -- actually being better for low power/big area situations, are a third, more different approach.

IMO, it is kind of important to at least 'hear' about the differences in these kinds of discussions -- not to gloss over too much, but then finally IN THE SHORT TERM 'hear' the simpler explanation.  Eventually, that more complete/complex explanation will percolate into the brain :-).  Some people will never need to general idea of the more accurate/complicated view, but those who would be interested are starting with fewer 'short circuits' in their thinking.  I admit that being totally accurate is both impossible to comprehend and frankly it is impossible for me (or probably most of us on this forum) to be accurate simply due to memory, knowledge or simple amount of time to explain!!! :-).

John Dyson

Re: 101 sound question: bass from a small speaker or how high is that wave?

Reply #11
Does someone know why, say, 50Hz bass from speakers sounds lower than 30Hz bass from headphones? Or generally, same frequency bass sounds lower on speakers than on headphones.

Or is this some form of placebo?

Re: 101 sound question: bass from a small speaker or how high is that wave?

Reply #12
I don't know a scientific answer why a speaker sounds 'bassier' than a headphone other than the speaker transmit the sound more to the whole body than a headphone.   Maybe that is the reason?   I agree that there is something more satisfying about true bass from speakers.

Re: 101 sound question: bass from a small speaker or how high is that wave?

Reply #13
Does someone know why, say, 50Hz bass from speakers sounds lower than 30Hz bass from headphones? Or generally, same frequency bass sounds lower on speakers than on headphones.

Or is this some form of placebo?

There is a well known psychoacoustic effect where people will falsely perceive a  harmonic as the fundamental.

https://en.wikipedia.org/wiki/Missing_fundamental

This is highly relevant because the most common form of distortion of bass frequencies by overdriven loudspeakers is the generation of false second and third harmonics.

Second harmonics commonly relate to a voice coil that is off center in the magnetic field along the longitudinal axis of the voice coil. This can be the result of a faulty design or manufacturing errors.

Third harmonics commonly relate to a voice coil that is driven out of the effective range of the field magnet assembly. A well-designed speaker will have this designed-in so that the speaker is protected from permanent damage by being overdriven.

Most natural musical deep bass sounds tend to have more energy in their harmonics than the fundamental and tend to be excited by single notes due to their narrow frequency range and musical values. So IM is less of a concern and low order harmonics tend to be tolerated by the ear and brain.

 
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