Monday, September 17, 2012

The Science of Music -- Part Three

So far we’ve learned about waves -- sine waves -- and complex waves made up of sine waves. You may know or have guessed that this has something to do with music. You are right. It has everything to do with music. Music is just a special kind of sound. Speech is a special kind of sound. Police sirens are a special kind of sound. The ocean roaring up the beach is a special kind of sound. And, MUSIC is a special kind of sound.

So what is “sound.” That’s a good question, and one we will answer with this episode of the “Science of Music,” or would that be “The Sound of Music.” Cue Julie Andrews:

If you want to follow me, you've got to play pinball
And put in your earplugs, put on your eyeshades
You know where to put the cork

Listening to you, I get the music
Gazing at you, I get the heat
Following you, I climb the mountains
I get excitement at your feet

So just what is music, or sound for that matter. Well, sound is a wave, a sound wave. Let’s start the explanation with a visual example -- in your mind.

Imagine a calm pool of water. Now mentally drop a stone into the center of the water. The stone causes a disturbance in the smooth surface of the water, and this disturbance spreads out in all directions from the point of impact. If you look very close at the “wave” spreading out from the point where the stone hit, you’ll note that it consists of a part that is a little higher than the normal water surface followed by a point a little lower. The higher part is called the “crest” and the lower part the “trough.” It is a wave, and it moves across the pond. In engineering speak, we would say the wave “propagates.”

If you look closely at the wave you can see it has a “wavelength,” the distance between two crests. You’ll also note that it has a speed of propagation, a velocity that it moves across the water. Finally, you may note that it will bounce off or reflect off of solid objects it encounters in its path. You may even see the result of the initial wave and the reflected wave adding together. Now this addition is quite interesting because, depending on the phase of the wave where it meets another, the crests may join and get bigger or the troughs may join and get deeper, OR ... a crest may add to a trough, effectively subtracting and resulting in water at the original pond level.

You have just experienced, in your mind, many of the characteristics of waves and wave propagation, and wave reflection including wave addition (which might end up being subtraction).

Sound waves have many of the same properties as these water waves you have been imagining. There is one big difference, however (in addition to the fact you can’t see sound waves). Water waves are "transverse," while sound waves are "longitudinal." Now there’s a couple of fifty-cent words! Transverse means they are “up and down.” The water waves were at right angles to the direction of travel or propagation. The water waves consisted of highs called crests and lows called troughs.

Sound waves occur in the same direction as propagation. To understand that, we have to understand what makes a sound wave. The answer is quite simple: vibration. It can even be that simple harmonic motion I mentioned earlier. Imagine a tuning fork. That’s a rod with a forked end that is made to vibrate by striking it. Then the ends of the fork will vibrate to and fro. As they do that, they will have an effect on the air around them. Viewing the tuning fork from one side, you can imagine the fork moving toward you and, thereby, compressing the air a little more than the average air pressure. An instant later the fork moves away from you and that has the opposite effect. It reduces the pressure of the air slightly below the average air pressure value. Now these “more pressure” and “less pressure” effects move away from the tuning fork just like the waves moved away from where you dropped the rock in the pond.

These “sound waves” which are alternations between air pressure higher than “ambient” or average air pressure -- call these higher pressure areas “crests” and lower air pressure which are the troughs -- are just like the ripples in the pond.

The difference is that the crests and troughs are in the direction the sound is moving: “longitudinal,” instead of up and down (transverse) like the water waves.

So there you have it. Sound waves are just pressure waves moving through the air. Now sound can also be conducted through water or solid objects, but -- unless you are listening to your iPod underwater or by putting your ear on a railroad track, we’re only going to focus on sound waves moving through the air.

Later we’ll talk about the ear and how it responds to sound waves. But, let’s dig a little deeper into these waves in the air we’ve just imagined.

First let’s turn to the American Heritage Dictionary of the English Language, Fourth Edition, for a very precise definition of sound. Quoting from Wikipedia’s quoting from the dictionary, we read, “Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.”

That is a good definition. Yes, sound is a mechanical wave, often called an acoustic wave. Also it is an oscillation or “vibration” and it is transmitted by pressure waves. To be very clear, sound is frequencies we can hear. There is also sound we can’t hear, often called ultrasonics, and they can be heard by other animals like dogs, porpoise, and bats, as well as they can be used to clean jewelry. Finally, to classify as sound, it has to be audible. That means loud enough to hear. You know what? This paragraph probably has at least five episodes of this series contained in it. We will come back to many of these ideas. This sound is some “Good Vibrations.”

While we’re being so scientific, we can mention that the waves propagate or move at, get ready for it, ... the “speed of sound.” That’s about 1,000 feet per second or one mile in five seconds. That’s pretty fast, although light is much, much faster. Light and electric signals travel at 186,000 miles per second. Also, sound level or loudness can be measured as a “sound pressure level” or SPL, which is the difference, in a given medium, between average local pressure and the pressure in the sound wave.

If we go back to the pond example, if the pond is very large, then the intensity of the ripple waves will decline until it just disappears. On a large pond, a rock dropped in one end may not even show waves at the other end. Same with sound waves. They gradually lose their intensity and die out. You can hear someone talking at the dinner table, but not someone talking down the block -- unless they’re really, really loud. We referred to this gradual loss of intensity a couple of articles ago when we talked about a damped waveform. Remember the swing. If you don’t keep pushing it, it will eventually stop swinging.

Also recall from the pond example that, just like water waves, sound waves can be reflected by hard surfaces and bounce back and add (or subtract) to other waves. All these effects of reflection and sound wave interaction (called, among other things, vector addition) can produce all sorts of interesting “acoustical” effects. That is why the physical design of a concert hall is so important. That’s also why you can hear an echo when you yell “hello” into the Grand Canyon.

One final topic for today: Sound vs. Noise. Now, just as one man’s garbage is another man’s treasure, the difference between sound (or music) and noise is what you want to hear. At that concert, the sound (or music) is coming from the band or orchestra. The noise is coming from those people in the seat behind you that know all the words and insist on singing them loudly. It’s all relative. After all, it might be your brother-in-law in those seats behind you. (Oh, humor: argh argh.)

When we start recording and amplifying and storing sound (or music), the electronic devices may add noise of their own. Hopefully, the amount of noise (or random signal) added will be too soft to hear. Remember the definition of sound is what is loud enough to hear. So what matters with noise is how loud it is relative to the sound we want to hear. We call that the “signal to noise” ratio or “S/N.” One solution is to have a very high or loud “signal” to drown out the “noise.” Even better is to have very little “noise.” Note that, when you amplify a small or quiet or soft signal to increase its volume or loudness, you are also amplifying the noise. So noise in the “front end” or input part of our sound system matters the most.

Now, for the conclusion, which should be expected. All sound (or music) AND noise, are just made up of sine waves. They are complex waves, for certain, but we already know that all complex waves are just made up of a fundamental frequency plus harmonics. Complicated sound (or music), like that from a band or orchestra, will contain lots of individual tones, each with a fundamental frequency and harmonics. So it gets very, very complicated. Separating the sound (or music) from the noise is often done by selecting certain frequencies. You know, the “tone control” or as we engineers call it, “equalization.”

And that will be the topic of the next episode of “The ... (echo, echo), Science ... (echo, echo), of ... (echo, echo), Music ... (echo, echo.)

Originally written on Feb. 17, 2012 during a visit to my Dad's home in Hillsboro, Oregon and posted on Facebook. During my two week visit with my dad, I wrote an article a day. I started with a long series on the Science of Photography which had thirteen individual articles. I then started this series on the Science of Music. It isn't finished and I have a lot more to say. I hope to add to this series in the future.

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