Guest wrote:I'm building one now for maximum resonance, with an 1/8" tapa front and back, so I can play the back without snare. I suspect this will be louder than a thicker back, since the back will resonate along with the tapa, granted there are cancellations at some frequencies when you do this.
It sounds like what you're going for is a longer ringing of the tapa tone... I too can see this happening with the double tapa thing (though i'm not sure -- i wonder if the cancellation you mention might foil that plan), but I suspect the deep sub-80 Hz "kick" sound will be a little weaker and shorter (and lower in pitch) with a double tapa. Excited to hear what your results are like.
"But if I put in 80Hz (right in the middle of the measured resonance of my cajon), it yields 2.26 inches (even 87Hz yields 1.6 inches), implying to me that maybe the model is not so accurate?"
Not sure I follow. The port dimensions are not altering, much, the fundamental resonance of the tapa, they are determining the resonance of the ported system
Yeah - with all the various frequencies I gave (except where explicitly describing the tapa) I was talking about the air spring / cavity resonance, not the tapa resonance. When I play my tapa, I hit it with the full weight of my flat hand, and my hand stays there: that is to say, the tapa doesn't vibrate at all -- not even once cycle -- it's fully damped. It's used as a driver of the air spring of the box, but not like a vibrating membrane drum. This is how many/most of the players I've seen play their cajons (or their tapas are so dead that the resonance is moot anyway). I have seen some more traditional players in afro-cuban ensembles play it more like a drum head, where the ringing tapa is part of the sound. It's surely more "proper" and correct to do so, but I'm using the cajon as a kick/snare simulation, really, so I have slightly different design goals. My suspicion is that the 1/8th-inch plywood is more ringy at the more traditional smaller sizes as well, but i don't have direct experience with that.
E.g. this dude plays the "kick" version at 3:39, and the more traditional "doon" sound at 1:09: http://www.youtube.com/watch?v=ngGcNeKpZjE
I was guessing that the OP was looking for a sound more like this guy at 4:51: http://www.youtube.com/watch?v=dpReSnkGrTU
...whose cajon seems to have a naturally dead kick sound.
"I wouldn't be surprised if the forumla they use assumes a port of some significant length and the real-world accuracy drops off as the port goes to zero?"
There are error factors, but the calculations are theoretically sound, even those that yield negative port lengths! The main reason the port length isn't critical is that the volume is so large and we aren't trying to tune it very low. A typical speaker might be half this volume and we try to tune the port to 50Hz...much trickier.
My point is that the helmholtz equation is an approximation of a complex system that makes certain simplifications; as the operating parameters get near the edge of the envelope that the equation is designed for, it gets shaky.
Classic Helmholtz visualizes the air in the neck of the port as a mass weighing on the spring of the air in the cavity. The formula:
f = (v/2pi) * sqrt(A/V*L)
...where v is speed of sound, A is area of the port, V is the volume of the cavity, and L is the length of the port. We can see that as L goes to zero, the resonant frequency of this idealized cavity goes to infinity, which is obviously not the case! Put another way, the aerodynamics of air in a tube are totally different than air through an opening in a membrane, and with port length going to zero we're crossing into that territory. I conclude from this that classic Helmholtz is not appropriate for short port lengths. This same kind of formula is in evidence at the link you sent: it's solving for L, but you can see that as the desired resonant frequency gets close to a certain limit the change in port length becomes vanishingly minute.
From the link I posted above: "the air in the body of a guitar acts almost like a Helmholtz oscillator. This case is complicated [...] because the air 'in' the sound hole of the guitar has a geometry that is less easily visualised than that in the neck of a bottle."
This is why they use a variation on Helmholtz that they describe, because you can't visualize the 2mm-thick top of the guitar as a very short port, the equation just doesn't hold up well at that extreme.
For my cajon (with a "port" length of 1/2 inches), classic helmholtz says the frequency of the cavity is 282 Hz (this is all in meters):
(340/(2*pi))*sqrt((pi*(.079375^2))/(.508*.3429*.3302*.0127)) = 281.677
...which is clearly not the reality. But with a port just 0.5 inches longer (1 inch) that drops to 200 Hz -- a 81 Hz difference if I use 1 inch plywood instead of 1/2 inch? -- not likely. Using 1/4-inch would supposedly take the resonance to almost 400 Hz. 2 inches drops it to 140 Hz. A bit more credible, but I'm still not sure I trust that equation until the port is 5 or so inches long, if it's even accurate then. I assume the equation on the site you linked to probably uses some reflex-port equation variant that is more accurate at short port lengths (since people aren't building speakers with 4-foot long ports typically) and for speaker sizes/shapes, but it still demonstrates this same basic pattern of hypersensitivty toward the extremes.
The equation from my link, which is tailored for measuring guitar cavity resonance, which IMO is a closer model than a bass reflex port system, yields 87.5 Hz, which is right around what I measured in my cajon. I don't know what version they're using on this reflex-cabinet calculator: http://www.lautsprechershop.de/index_hi ... ltz_en.htm
...but that link gives me 89.7 Hz with a 1/2 inch port and 90 Hz with a 0-inch port, which lines up well, and shows that they're using something besides regular helmholtz.
For me the upshot is: build it so you can change it later. :-) Even if we had the perfect equation, there are plenty of uncertainties that we're going to need to adjust for.
"...takes it down probably to 60 or so: awesomely deep, but also kinda weird and not always appropriate for the song somehow"
I think this is the issue with the OP. He's stumbled on a highly resonant tuned system, and it's too boomy.
Yeah, agreed. I assumed the OP was hearing more "doon" resonance in general from the tapa when they were expecting more of a dead-thud kick sound. If we haven't scared the OP away, maybe they will let us know what they are looking for. :-)
I look forward to posting my results to your site.