Instrument Physics II: Funny Lines

Waves. They’re pretty cool, and vital to understanding instruments. Those little funny lines represent the way we see things, the way we hear things, and probably more but I didn’t pay attention in biology. 

If you’ve read the last blog related to it, you’d already know about concepts like medium, wave speed, and the such. If you haven’t, I highly recommend reading that one as well. You can find it here: Instrument Physics I: The "Wave"

Constructive and Destructive Interference:

To understand how an instrument makes sound, we really need to understand what wave interference is. Wave interference is when two waves overlap with each other. They add together and make a new wave altogether. 

When waves oscillate, this occurs in time. Since oscillation happens in time, two identical waves can oscillate in sync with each other, out of sync with each other, or somewhere in between. 

There are two different types of interference too: constructive and destructive. Of course, two waves interfering don’t have to be only one or the other, they can be a combination of both constructive and destructive interference. 

As for constructive interference, it occurs when two waves are oscillating in sync and they overlap. Here’s an example of two identical waves that are in sync going through constructive interference. As you can see, when they add together, they make a new wave that’s more intense! If this wave were a sound wave, it would result in a louder sound. (Helpful note: the green wave is equal to the blue wave plus the red wave)

Destructive interference is the exact opposite of constructive interference. When two waves that are out of sync overlap, they completely destroy each other. Here’s an example of two identical waves that are out of sync going through destructive interference. As you can see, when they add together they make a new wave that might as well not be there. In sound, destructive interference results in a softer sound. (Again, the green wave is just the red wave plus the blue wave)


Interference Between Waves of Different Frequencies:

Ok so this part isn’t important to understanding how instruments make music, but it’s cool to look at and I like showing people cool physics stuff, so here we are anyway. You could skip this if you wanted, but that would be lame. 

What’s really cool about waves is that they interfere even when there’s several different frequencies interfering. This is when waves interfere with each other both constructively and destructively. 

Let’s look at a simple example first: the octave. An octave, in music, is two notes where one has double the frequency of the other. When they interfere, they have some parts that overlap constructively and some parts that overlap destructively. (Remember: the green wave is the red wave plus the blue wave.)

Interference like this is also how chords (groups of several notes) are formed! Here’s an example of a C Major chord (the notes C, E, and G) all interfered together. Now, when they interfere, it just looks even crazier. (Again, the green is just the red plus the blue plus the purple.)

Does it necessarily have anything to do with how an instrument makes music? Nope, but I put it here anyway and there’s nothing you can do to stop me. Unless the wonderful editor takes this out. That could stop me. 

Standing Waves:

We give names to several specific phenomena. A wave bouncing off of a surface is called a reflection, or maybe an echo. One interesting phenomenon that waves on a string use is called a standing wave. 

Imagine we have a big slinky on the ground and one end is being held by someone. Now, we go to the other end and send a pulse down the slinky. The pulse will travel down to the end being held by someone, reflect off of their end and come back to you. Let’s say you were to consistently send a wave going through the slinky by repeatedly shaking your end. What would happen? Of course, the waves would travel down the slinky and then come back to you, but then something special happens. The wave you send down will interfere with the waves reflecting off the other end. When they interfere, some insane stuff starts happening. 

Below is a GIF of a wave traveling to the right (the wave you sent down the wave), and a wave traveling to the left (the wave that’s reflected off the other end of the slinky). Below that is the wave that’s the result of the interference of the two waves moving. This bottom wave is what the string will look like as the two moving waves interfere. Look to see what happens (thanks to the University of Wisconsin-Stevens Point for the GIF!). 

The new wave looks like it doesn’t move! If you look, there are points along the wave that are always at zero (we call these nodes) and points along the wave that are always at the maximum value (we call these antinodes). You can see these points pointed out on the GIF, with the node being the left point and the antinode being the right point. 

Standing waves are pretty crazy, but their relationship with the actual parts of a wave are even crazier. In the example above, there was a clear wavelength to the standing wave. The wavelength of a standing wave is directly related to the length of the string the standing wave is on. So, if you increase the length of the string, you increase the wavelength of the standing wave. The wavelength of a standing wave is dependent on one other thing, however, and that’s the number of antinodes that are present on the string. Because of how we’re looking at standing waves, they don’t really matter, so we can ignore that value. To understand their relationship we need to define our variables: length is L, the number of antinodes is n, and (like before) wavelength is λ. As an equation, a standing wave looks like this: 

λ = 2/n(L)

We can just ignore the number of antinodes since they don’t matter in this case and just look at how the wavelength and length of the string are related to each other. As we can see, if we increase the length of the string, the wavelength also increases. If we decrease the length, the wavelength also decreases. 

But wavelength can mean more than just how wide one oscillation is. It can also be the speed of the wave divided by the frequency of the wave, as we established earlier. So, if we increase the length of a string, then the wavelength will increase. If the wavelength increases, then either the speed must increase as well, or the frequency will have to decrease along with it. 

In the end, standing waves are one of the coolest wave behaviors out there (at least in my opinion). 

How this all applies:

I bet you thought I was gonna reveal how all of this works in an instrument now. Truth is, I was planning to. However, this blog is more than long enough, and doesn’t need to be any longer. So, I’m just going to end it here. See you next time!

Guest Writer: Benjamin Mellick, K.C. Strings Staff