Instrument Physics I: The “Wave”
We think string instruments are pretty incredible. It's hard for us to not think they are something extra fascinating since this is our passion. So whether you think strings instruments are intriguing or not, they have some really cool physic properties and we are excited to share more about it!
Instruments make sounds. Sounds are waves. Waves are pretty neat, but what are they?
In its purest form, a wave is the transfer of energy without the transfer of matter. That explanation is dull though, and sounds confusing (at least to me). Let’s think of people doing the “The Wave” in a sports stadium. If everyone cooperates, it looks amazing. However, if everyone does not follow along, the person attempting to start "The Wave" looks a bit strange. Ignoring that, let’s say everyone follows along. When they do, people stand up, then sit down. As the first group of people sit down, the next people stand up, and then sit down. As the next people sit down, the next next people stand up, and the cycle continues. It looks like there’s this thing moving across the stadium, but there’s not a group of people just constantly running around. The “Wave” is moving around the stadium (there’s our transfer of energy), but the people don’t leave their spots (there's our “no transfer of matter”!). The “The Wave” is the perfect example of what a wave is.
Sound is the same way! Sound is a wave that can move through basically anything. I don’t know about you, but I usually hear sounds moving through the air. When we hear a sound, some kind of energy has to move, but my ears are not constantly filling up with air. If they were, my head would explode! So how does sound move energy? By using a wave to tell our ears what to hear.
“How does a wave move energy without moving matter?” you may be asking yourself or, more likely, me.
I don’t know.
At least that’s what I would say if I didn’t know about oscillation! Waves move via oscillation.
Oscillation is an intimidating science word that basically means, “moving, but in a special way.” For its actual scientific definition would be: oscillation occurs when an object moves back and forth around a single point. If someone were to jump with a jump rope, they would have jumped. However, if they were to jump rope (the verb this time), they would be jumping up and down. In this case, the jumping jump roper would be oscillating up and down.
“How does this affect waves?” you may be wondering. It’s actually very simple. Particles are like little pinballs connected by loose strings. If you were to move one back and forth, the string would stretch out and pull other pinballs with it, or the string would collapse as the pinballs hit each other, causing more movement. Then, the string is stretched too far, and the pinballs are pulled backwards again.
“What even is an oscillation though? How do we define it?” you find yourself asking. Good question. A complete oscillation is when the thing oscillating returns to its original condition. For example, the jump roper must return to the ground and be headed up again, just the way they were when they started jumping rope. The jump roper returned to their original starting condition, which is necessary for counting one full oscillation.
But waves can’t exist without something to move through, surely there’s got to be something that has to do with that!
There is. It’s called the wave’s medium. It’s just whatever the wave travels through. For the “The Wave”, the medium would be the crowd. For sound in the air, it’s the air. The medium of a wave can be literally anything! For light, for example it’s both electricity and magnetism. For earthquakes, their medium is the crust of the Earth, the part we all live on. The medium is just whatever a wave moves through.
The Parts of a Wave:
Everything has its components. Glasses have lens strength, frame size, and color. Waves are the same way! Waves have several different attributes, including the frequency, the wave speed, and the wavelength. And, each one has a special relationship with each other.
What is frequency? To define frequency, we should probably define what the period of a wave is. In a wave, a period is the length of time a wave takes to do one oscillation. Usually, we measure periods in waves by time. So, if a wave has one oscillation every two seconds, its period is two seconds. The frequency of a wave is how many oscillations a wave can do in one second, it’s the opposite of the period (divide the number one by the period of a wave and that’s your frequency). Since it’s the opposite of a period, we also measure it with the opposite of a second, a “per second,” also called a “Hertz.” So, if a wave has a period of two seconds, its frequency would be one half Hertz (one half of a complete oscillation every second).
To better illustrate the differences in frequency, a picture of several waves is provided below. Every number marked by the bottom line represents one second. That would mean the green wave has the highest frequency of one oscillation per second, the blue has the second highest frequency at one half of an oscillation per second, and the red has the lowest frequency of one fourth of an oscillation per second. The higher the number of oscillations per second, the higher the frequency.
What about speed? What is that? Well, the speed of the wave is how fast it can pass through what it’s going through. Let’s look at sound in air. A sound is produced, and some air particles oscillate. These particles then make other particles oscillate, and those make other particles oscillate, and so on. Sound actually travels faster the denser the medium. Steel, for example, has a ton more particles in one given space than air, so sound will travel faster through steel than it does through air. The speed of the wave (or just “wave speed”) is how quickly the particles can cause other particles to oscillate. As the wave physically changes position, we can give it a speed. Going back to the speed of sound in air, for example, is about 343 meters per second, or 767 miles per hour.
So we know what frequency and speed are, but what does wavelength even mean? We’ve already defined that a wave moves, and that the particles in a wave oscillate. To define wavelength, let’s look at sound again. As mentioned before, a sound wave has parts where there’s a lot of particles and parts where there’s almost no particles. The wavelength is the distance one full oscillation occurs in. Take the picture used for frequency as an example. Let’s say that, instead of the numbers at the bottom representing seconds, they represent feet. That would mean the green wave has a wavelength of one foot, the blue wave would have a wavelength of two feet, and the red wave would have a wavelength of four feet.
How do these make up a wave though? Unlike everything else so far, it’s actually not that complicated. The speed of the wave (v) is equal to exactly the frequency of the wave (f) times the wavelength of the wave (λ). Represented as an equation, it looks like this:
v = f
What does this mean? Well, if you were to increase the wavelength, the frequency would have to also decrease to keep everything equal. If, instead, the frequency were to increase, the wavelength would then have to decrease for the equation to actually be true. Finally, if the speed increases, then either the wavelength, frequency, or both would have to increase as well.
Sound and the Difference Between Longitudinal and Transverse Waves:
There is one final thing we need to understand to understand an instrument, and that’s sound. It’s been mentioned several times that sound is just a wave, but it’s not the kind of wave most people would think of.
Some waves, like the “The Wave” are called transverse waves. That means the direction of the oscillation (like the way the people move when doing the “The Wave”) is perpendicular to the direction the wave moves. To go back to the “The Wave”, the people partaking in it are moving up and down while the “The Wave” is moving side to side. Another example of transverse waves would be ocean waves, with the water moving up and down but the wave moving side to side.
Other waves, like sound waves, are called longitudinal waves. Instead of the parts of the wave oscillating perpendicular to the direction the wave moves, the objects oscillate parallel to the wave’s movement. If a sound wave travels through air to the left, then the air particles will oscillate left and right. If the wave moves up, the particles will oscillate up and down. That’s why speakers (if you can see the parts that actually make a noise) push forward and pull backward. They’re moving air and making sound.
To help create a better mental model, here’s a GIF I found on the internet to illustrate the differences between a transverse wave and a longitudinal wave.
Well wow. That was a lot, and I haven’t hardly mentioned instruments yet! However, that was a lot of stuff to write, and even more to read. So, I’m going to call it here. Tune in next time to take the next step into how instruments make beautiful music.