Yup, the wide world of subs is an interesting, and sometimes overwhelming place
One thing to know is that we humans don't really hear bass very well. We kinda suck at it, really

Our hearing at different frequencies is not linear. At low volumes, we can hear mid-range frequencies ok (the range of the human voice), but at the very same volume, we can barely hear bass notes at all! Turn up the SPL (Sound Pressure Level) to 85dB and our hearing from 20Hz (the lowest note that a human with healthy hearing can detect - give or take a Hertz or two

) on up to 20,000Hz (the highest note we can detect, although after about age 15, this starts to get lower. Most adults can't hear much over 15,000Hz. A lot of people can't even hear that high. Remember though that every doubling of frequency is only one octave. So while 40Hz is one octave higher than 20Hz; 20,000Hz is only one octave higher than 10,000Hz!) is pretty much linear. So an 85dB 25Hz note will subjectively sound about as loud as an 85dB 1,000Hz note, and subjectively about as loud as any other 85dB note from 20Hz on up to 20,000Hz. FYI, that is why "reference" volume level is a nominal 85dB with dynamic peaks as loud as 105dB and dynamic peaks in the low bass as loud as 115dB - since, once again, above 85dB, our hearing stops being linear again
Anywho, all of that preamble is to say that when it comes to a subwoofer, our limited human hearing really only responds to three primary attributes: depth of bass (how low the subwoofer can play), loudness of bass, and transient response (how quickly the bass notes start and stop). Those are sort of the three key aspects of bass performance that are really important to consider in a subwoofer. So when we talk about one subwoofer being "better" than another, it's mostly going to be about either being able to play lower, play louder, or play with better transient response - which will often bring up words like "clean" or "tight" or on the flipside, "bloat" or "overhang" or "muddy".
Of course, there is also linearity and accuracy to consider. If the signal going to your subwoofer is telling it to play a 95dB note at 65Hz, it would be nice if the subwoofer actually played that correct note at the correct volume, yes?
Linearity is a very tricky matter because the subwoofer itself might or might not be linear, but the room acoustics also play a HUGE role in how linear the subwoofer will sound when it is placed in a given spot in the room and you are listening from a given spot in that room. If you move, or the subwoofer is moved, the response that you hear can totally change! The subwoofer won't be playing any differently, but due to the fact that bass interacts very strongly with the room, the room's acoustics will strongly affect what you actually hear.
So a perfectly linear sub is nice - it's always good to start with a subwoofer that plays linearly when it is all by itself, without the effects of the room's acoustics acting on it. But it's important to remember that even the most linear subwoofer will not SOUND linear in a room. So being perfectly linear isn't always of paramount importance in a sub. If you want to HEAR linear bass in your room, you're going to have to make adjustments anyway.
Accuracy is a different matter. You definitely want your subwoofer to be accurate. When the signal says to play a certain note, that's the note you want your subwoofer to play! With very cheap subwoofers, you will often hear them described as being "one note" subwoofers, or maybe just "inaccurate". A lot of very cheap subwoofers simply do not play the notes that they are asked to play. That's a REALLY bad thing, and something you should want to avoid completely!
So with that out of the way, what are some other things to consider with a subwoofer?
Well, there is physical size, whether the subwoofer is sealed or has a port (or several ports), how big the driver is, how powerful the amplifier is. And how all of that stuff works together to make a sub that can play low, play loud, play with good transient response, and play linearly and with high accuracy...or not
One thing to know is that the primary job of a subwoofer is to move air. Sound is just moving matter. If we want to make a loud noise, we have to move a lot of air! And the lower the note, the more air we have to move in order to make it sound just as loud as a higher note. In other words, low, loud notes require the movement of A LOT of air!
So how do we want to move the air? Do we want to move it efficiently? If we do, then it makes sense to use a big driver. A 15" woofer has a lot more surface area than a 10" driver, so it already has an advantage when it comes to moving more air. That 10" driver COULD move just as much air as that bigger 15" driver, but in order to do so, it's going to have to move in and out (called the excursion) a lot more. So the big 15" driver can move a little, but in order to sound just as loud, the 10" driver would have to move a lot!
Moving something a lot requires more power from the amplifier. So even though you might think that you need more power to move a big driver, it's actually the other way around! You only have to move that big driver a little bit, so that doesn't take as much power. With the smaller driver, if you want it to play just as loud, you have to move it a lot, so that takes more power. In other words, just saying "a 400 Watt" amp doesn't tell you the whole story. A 400 Watt amp connected to a 10" driver isn't going to move as much air as that same 400Watt amp connected to a bigger 15" driver.
Of course, a bigger driver is going to need a bigger box. If you want a small box, you have to use a smaller driver. And if you want that smaller box and smaller driver to play just as loud as the big driver in a big box, you're going to have to use a much more powerful amp in the SMALL box so that you can move that small driver a lot more!
That's the basics, but there is one more thing to consider. The box itself can help to reinforce the sound that the driver is making. Just like the body of an acoustic guitar amplifies the sound made by the guitar string, the box of the subwoofer can be used as a chamber that resonates and amplifies the sound made by the subwoofer driver. And just like the body of an acoustic guitar, if you want the box of the subwoofer to amplify the sound in this way, it has to have a hole in it - which on a subwoofer, is called a port.
So a ported subwoofer is more efficient in terms of how loud it can play vs a sealed subwoofer. With a sealed subwoofer, you are relying entirely on the movement of the subwoofer driver to move the air and create all the sound. With a ported subwoofer, the box of the subwoofer comes into play and amplifies the sound through resonance.
Now, a big box is going to resonate at a lower frequency than a small box. So again, a small box makes things tough. A very efficient way to make a subwoofer is to use a fairly small driver and a fairly low-power amp, but to put them in a BIG ported box! The small driver with the small amp won't move very much air all on their own, but that big ported box will resonate at low frequencies and amplify the small output of the small driver and small amp.
Naturally, if you put a big driver with a big amp in a big ported box, you can get MASSIVE output! Put a small driver with a small amp in a small box - even a ported one - and the output will be quiet. So...most subwoofers fall somewhere in the middle. Maybe small driver, small sealed box, HUGE amp. Or maybe big driver, medium-sized sealed box, medium amp. Or maybe medium driver, medium amp, big ported box! It's all about compromises. But it's all about moving the air, and it's just a matter of choosing how you're going to accomplish that!
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