Dayton Audio BR-1 Speaker Build

This post is not meant to give you detailed instructions on the BR-1 assembly. The professionals have already done that here: https://www.youtube.com/watch?v=t_e1Ex8yJ6g and here: https://www.youtube.com/watch?v=c-N_vx6oOVE.
However, my experience of building the kit was not quite as simple as they’ll have you think from watching those tutorial videos. This post will be a good supplement to anyone who is building the kit. It has some work arounds for when you don’t have all the right tools, and some tricks I found useful along the way.

TOOLS

You’ll also seed a hot glue gun and a crimp tool.

CROSSOVER

I arrange my components like this to ensure that I don’t make a mistake. You’ll also notice my special high quality wire cutting tool: fingernail clippers. If you don’t have wire cutters that can make a cut that is flush with your solder joint, fingernail clippers are a great work around. It’s important to  clip the wires flush with the joint in order to glue the crossover to the cabinet later.

WIRES

Mark your cable before you cut so you don’t make any mistakes. I also took a sharpie and marked one side of each cable black for negative, so that I don’t make polarity mistakes later when the crossover circuit is difficult to see.

ACOUSTIC FOAM INTERIOR

When you’re cutting your foam, proportions are more important than exact inches because the piece of foam they give you often isn’t exactly the right size. Maybe according to the manual, 9″ from one side is half way, but after you cut, you might find that your other piece is only 7 1/2″ wide. Darn. So find the halfway point for your particular piece of foam. I found that angling my knife away from the direction I was cutting made the cleanest edges.

PUTTING IT ALL TOGETHER

Here you can see that marking the cables was a really good idea as the crossover circuit gets completely covered with foam. I also marked the back of the cabinet for polarity. The polarity is marked on the terminal block, but it is hard to see on the black plastic. I also found that I didn’t need to use all of the foam they gave me to completely cover the interior of the cabinet, and once I got all the foam in there, it was held in place by friction and tension from all the other pieces of foam. I didn’t feel the need glue the foam into place. I’m only a bit worried about the top piece. I’ll probably go back and glue that one at a later time.

All done!

Comb Filtering in Rooms: Part 1

Comb filtering is a type of “interference.” Interference can be parsed into two categories: constructive and destructive.
       
In the graphs above, the bold line is the sum of mathematical signals. You might be wondering where the bold line is in the second graph. In the second graph, the sum of the two signals was destructive, and the amplitude of the signal was reduced to zero. In the first graph, the sum of the signals was constructive, and the amplitude increased by a factor of 3. The featured image at the top of this post shows the two individual signals that were summed to make the second graph. When one is up, the other is down, and always by the same amount. Imagine that the bold line is a copy of the lighter line that we dragged to the left. We can describe this mathematically by saying the signals are 180° out of phase. But imagine that we kept dragging the bold line farther and farther to the left. The two lines would eventually line up with each other (now you’ve shifted the signal 360°). If we kept going, they would become out of phase again (now you’ve shifted the signal 540°). When a copy of a signal is shifted by an odd number multiple of 180° and summed with the original signal, the signals will cancel with each other. This is the basis of comb filtering.

Until now we’ve been talking about shifting signals in terms of degrees. Now we are going to talk about shifting signals in time. Delaying a signal by 180° is equivalent to delaying it by half of the signal’s period. Let’s imagine that we’re listening to a piece of music on a pair of speakers. The spectrum of human hearing ranges from 20Hz to 20,000Hz. Now we move one speaker so that it is one foot farther from our ears than the other speaker. We have now delayed one signal. Given that each speaker is likely producing frequencies from around 40Hz to 18,000Hz, it is likely that the delay we created is half of the period of some frequency, and is therefore being canceled. It is also likely that other frequency’s half periods are odd numbered multiples of the delay, and will be canceled as well. Can you guess which ones? I can’t! So I derived a mathematical formula for it.

First, we need an expression for an odd number multiple. Any number multiplied by 2 is even. Any even number plus 1 is odd. So (2n+1), (where n is a whole number greater than or equal to 0; n = 0, 1, 2, 3, …) is an expression for odd number multiples. We are interested in situations where a signal is delayed by half of the frequency’s period. So here’s the math.

Delay = Δ seconds;  Period = T seconds; Frequency = f Hz  (Δ is the capital greek letter “Delta.”)

Δ/T = (180°(2n+1)) / 360° –This is a ratio that says our delay divided by our period is the same as an odd number multiple of 180° divided by 360°.

*******You might wonder why I don’t say Δ/T = (1/2)(2n+1). After all, that expression means that the delay is half of the period and is much simpler. I’m using the degrees to relate it to what we learned about interference before.********

You might know that T = 1 / f.

So f*Δ=(180°(2n+1)) / 360°

HERE’S THE FORMULA

Therefore: f = (180°(2n+1)) / (360°*Δ)   Now just plug in your delay time and values of n to find out which frequencies are canceled.

Let’s say your copied signal is delayed by .0005 seconds (aka half a millisecond). When n = 0,1,2,3,4,… f = 1000,3000,5000,7000,… respectively.

Ouch. Those are all frequencies you’d want to be hearing when you’re mixing audio. Comb filtering is something we should be concerned about.

Now we know how time delay corresponds to frequency cancellation. But how does time delay happen in listening environments? One obvious place is the difference in distance from your speakers to your ears, but a more subtle case is reflections from walls. This will be the subject of the next post.

Introduction

Hi! My name is Brian Kelley. Welcome to my blog!

This blog is where I will chronicle my adventures into the world of DIY audio. I have two main goals for the blog. I want this blog to be interesting to readers who already have a working knowledge of the subjects I will discuss. I will do this by including math and physics that could be interesting to readers with less formal backgrounds. However, I don’t want to write at a level that will exclude beginners. Although this is a blog about sound, I am passionate about the idea that language should never exclude anyone. I will try to use jargon minimally, and I will try to write as clearly and simply as possible- as I believe all writers should.

I’m currently assembling a pair of speakers that I’ll use for mixing. Later, I’ll work on positioning the speakers in my room, and acoustically treating the room. I’ll document that process in future posts, and I’ll also be publishing short articles on the physics that govern the decisions I make.

Stay tuned,
Brian