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An Equation for Subkick Resonant Frequency

Color me obsessed with subkicks, because I am. (Edit: check this article for info on free air resonance: http://blog.mixonline.com/mixblog/2012/01/12/diy-sub-kick/)

Having recently put into service on kick drum an NS-10 subkick, one of the first things I noticed was that the NS-10 sounded much deeper compared to the other woofer a coworker had rescued from the garbage. Since I have two subkicks of different size, I figured I might be able to find a function to predict the resonant frequency of other woofers. The first step was to determine what resonant frequency my Frankenstein mics actually put out, and then measure the size of the woofers.

Subkick #1 (Garbage)

I recorded a brief sample of me tapping on the woofer, and loaded it into Adobe Audition. Don’t bother listening to the audio clips unless your monitoring system or headphones extend down to 30 Hz.

You’ll notice that the frequency analysis pane shows a fundamental frequency of 64.59 Hz, while the bar graph shows very large bars all over that area. Audio editors can’t accurately analyze very low frequencies without very large FFT sizes, so the frequency analysis is an approximation. Since this simple waveform completes 5 cycles in 77 milliseconds, we can confirm the frequency the old fashioned way by using a simple algebraic equation and solving for x:

We’ll say the fundamental frequency of the garbage subkick is 65 Hz.

Measuring the moving parts of this speaker, I came up with a diameter of 4.75 inches.

Now onto the NS-10.

Subkick #2 (NS-10)

The first cycle of the NS-10’s waveform was asymmetrical, so I skipped it in favor of the clean sine wave that followed.

Using the same equation, 5 / 0.113 = 44.25 Hz. To get another result, I drilled down to 4 cycles.

4 divided by 0.091 gives us 43.48 Hz. The simple average of both results is 43.865; we’ll go with 44 Hz.

Measuring the elements of the speaker that actually move, I came up with a 6″ diameter.

Defining the Function

So now that we have two points, we should be able to find a simple linear equation to define the relationship.

Set 1: (4.75, 65)
Set 2: (6.00, 44)
Let y = ax + b
a =  (44-65) / (6-4.75) = (-21 / 1.25)
Substituting set 1:
65 = [(-21 / 1.25) * 5] + b
therefore, b = 144.8

Our equation is Resonant Frequency in Hz = (-21/1.25) * Woofer Diameter in inches + 144.8

So according to this drivel, if I had a 5 inch speaker, I should expect the resonant frequency when used as a subkick to be 60.8 Hz. Here’s a graph:

Now. This equation could be invalid for a few reasons. For one, a 9″ woofer wouldn’t resonate at -6 Hz (because that’s impossible). I’m sure a speaker designer could take a giant dump all over this, citing how I fail to include coefficients for thickness of the cone, material (eg. paper, plastic, other), mounting method, and probably a host of other variables I don’t even know about. THEY SHOULD PROBABLY PUT SOME INFO ABOUT THIS ON THE INTERNET, because God knows I couldn’t find anything when searching for it.

At the very least, this exercise provided a rudimentary definition of the size/frequency relationship between woofers that I own, and perhaps between woofers of similar construction and size (such as paper cones between 4 and 8 inches). If anyone would like to contribute measurements of their woofers, I’d be glad to plug in the data and refine the equation.

And now, here’s a video about Eve Online, an internet spaceship game.


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