Hi,
yeah there are equations, but you can easily test this in a cabinet simulator such as WinISD or any other that you can run on your computer so no need to get into math. There are likely some that work in a browser/mobile as well. These would show you results directly, as you can input exact parameters and see how they affect. But, is there audible differences? Depends on what you are doing, and what you have in mind.
In a domestic room (modes) would dominate the bass response and perception, so not sure if small changes in damping (system Q) matters much. There could be a room mode ringing in which case overdamping (reduced output at drivers resonance) actually makes sound better, not worse. There is a lot of electrical damping with low output impedance voltage amplifiers, but also any damping material inside the box dampens as well. Also resistance of the cabling and even EQ changes damping, so it's not box size alone that affects damping. Also system output is limited either by power handling (heat), or xmax, which ever limits it first. Reduced power handling means nothing if xmax is reached first, so also depends.
Since it's fun to think how driver in a closed box works as a system, here some more thoughts for anyone who wants to geek on it Got quite long, read if you fancy.
Increasing box size the max output of the system would stay relatively same, as output is how much volume displacement the driver does and ultimately limited by maximum displacement of the driver, which doesn't change here as it's physical property of the driver itself not function of the box size. System sensitivity would change though, in a bigger box less power is needed to reach max excursion as air inside the box is part of spring the driver motor does work against, and it loosens up as air volume is increased. When driver can handle enough power so that xmax is the limiting factor, max output of the driver can be reached.
The system is a spring mass resonator, where the spring consists of suspension of the driver and also of the air that is trapped inside the box.
If box was already quite big then change in box size might not be much at all, because driver suspension could already dominate the spring. If we assume air inside the box is significant part of the spring, then system Q value would drop some as you increase air volume, which basically means frequency response shape around system resonance would change less resonating, smoother, as the total spring loosens (more damped, could get "overdamped"). The resonant frequency also drops some when spring loosens.
Also system distortion might change a bit if driver suspension is highly non-linear, and you increase it's portion of total spring of the system by reducing portion of air spring. Another distortion source is heat, and bigger box means bit less power required for same acoustic output which means bit less heat. Heat increases voice coil resistance, which means compression and frequency response change (with low output impedance amplifier), system Q changes but basically the whole bandwidth is affected from heat. Also max output is reduced. In this sense, we'd want to design a system so that we need to input as little power as possible for desired output level, and now the power handling could become almost irrelevant concern.
So, unless I'm thinking it wrong the smaller your system (driver) is the more the box size matters, because the system is likely run with relatively high power to get enough excursion = get enough volume displacement = get enough SPL on some low frequency, and bigger box might be a good idea. On the other hand, if the cone is big the power required to get same volume displacement is likely less, so the box can be smaller. Simplified, you could increase size of your box or size of the driver in the same box, to get better system: more output at some low frequency before sound gets bad. Or use better driver, bigger driver, and multiple drivers to get more volume displacement. I'd say always use EQ to tailor system response (damping!), and handle room modal peaks.
And there is more, if application is bass for a multiway speaker increasing box size affects acoustics of the system because also outside of the box gets bigger and affects system response higher up in frequency, so it might be better to increase cone size instead, or at least be mindful of dimensions of the box. Standing waves inside the box might land on passband so woofer location on baffle could matter. Increased panel sizes mean that if they vibrate they make louder sound than smaller so box construction gets critical if you start to increase size of it, and bit less critical if you shrink it. Basically there is possibility to ruin mids if you only think bass. In general, bass in domestic rooms is dominated by room modes so what room you put it in and whether there is DSP available to shape the response, how much amp watts you have and so on, how many boxes the system consists of might also make some hints what the box should or could be, for any given driver. Or if the box needs to be particular size, you now must choose the driver wisely.
How much any of this matters? I don't know, depends what your goals are
yeah there are equations, but you can easily test this in a cabinet simulator such as WinISD or any other that you can run on your computer so no need to get into math. There are likely some that work in a browser/mobile as well. These would show you results directly, as you can input exact parameters and see how they affect. But, is there audible differences? Depends on what you are doing, and what you have in mind.
This needs to be read carefully, perhaps there is more in the book? These are relative metrics so not so simple the short quote lets first believe. Altgough how much any of this matters is also relative to who is listening, whats the application, for home or for garden party, or for a car, and so on
In a domestic room (modes) would dominate the bass response and perception, so not sure if small changes in damping (system Q) matters much. There could be a room mode ringing in which case overdamping (reduced output at drivers resonance) actually makes sound better, not worse. There is a lot of electrical damping with low output impedance voltage amplifiers, but also any damping material inside the box dampens as well. Also resistance of the cabling and even EQ changes damping, so it's not box size alone that affects damping. Also system output is limited either by power handling (heat), or xmax, which ever limits it first. Reduced power handling means nothing if xmax is reached first, so also depends.
Since it's fun to think how driver in a closed box works as a system, here some more thoughts for anyone who wants to geek on it
Got quite long, read if you fancy.Increasing box size the max output of the system would stay relatively same, as output is how much volume displacement the driver does and ultimately limited by maximum displacement of the driver, which doesn't change here as it's physical property of the driver itself not function of the box size. System sensitivity would change though, in a bigger box less power is needed to reach max excursion as air inside the box is part of spring the driver motor does work against, and it loosens up as air volume is increased. When driver can handle enough power so that xmax is the limiting factor, max output of the driver can be reached.
The system is a spring mass resonator, where the spring consists of suspension of the driver and also of the air that is trapped inside the box.
If box was already quite big then change in box size might not be much at all, because driver suspension could already dominate the spring. If we assume air inside the box is significant part of the spring, then system Q value would drop some as you increase air volume, which basically means frequency response shape around system resonance would change less resonating, smoother, as the total spring loosens (more damped, could get "overdamped"). The resonant frequency also drops some when spring loosens.
Also system distortion might change a bit if driver suspension is highly non-linear, and you increase it's portion of total spring of the system by reducing portion of air spring. Another distortion source is heat, and bigger box means bit less power required for same acoustic output which means bit less heat. Heat increases voice coil resistance, which means compression and frequency response change (with low output impedance amplifier), system Q changes but basically the whole bandwidth is affected from heat. Also max output is reduced. In this sense, we'd want to design a system so that we need to input as little power as possible for desired output level, and now the power handling could become almost irrelevant concern.
So, unless I'm thinking it wrong the smaller your system (driver) is the more the box size matters, because the system is likely run with relatively high power to get enough excursion = get enough volume displacement = get enough SPL on some low frequency, and bigger box might be a good idea. On the other hand, if the cone is big the power required to get same volume displacement is likely less, so the box can be smaller. Simplified, you could increase size of your box or size of the driver in the same box, to get better system: more output at some low frequency before sound gets bad. Or use better driver, bigger driver, and multiple drivers to get more volume displacement. I'd say always use EQ to tailor system response (damping!), and handle room modal peaks.
And there is more, if application is bass for a multiway speaker increasing box size affects acoustics of the system because also outside of the box gets bigger and affects system response higher up in frequency, so it might be better to increase cone size instead, or at least be mindful of dimensions of the box. Standing waves inside the box might land on passband so woofer location on baffle could matter. Increased panel sizes mean that if they vibrate they make louder sound than smaller so box construction gets critical if you start to increase size of it, and bit less critical if you shrink it. Basically there is possibility to ruin mids if you only think bass. In general, bass in domestic rooms is dominated by room modes so what room you put it in and whether there is DSP available to shape the response, how much amp watts you have and so on, how many boxes the system consists of might also make some hints what the box should or could be, for any given driver. Or if the box needs to be particular size, you now must choose the driver wisely.
How much any of this matters? I don't know, depends what your goals are
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If you end up with a speaker/box Q of .5 or less, the speaker system will lend itself to the use of a
'good old fashioned bass control' (if you have one). With this scenario you can achieve increased bass extension
( internal damping material becomes quite critical to good bass sound + you need an amp with enough power )
'good old fashioned bass control' (if you have one). With this scenario you can achieve increased bass extension
( internal damping material becomes quite critical to good bass sound + you need an amp with enough power )
