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About this Lesson
- Type: Video Tutorial
- Length: 11:43
- Media: Video/mp4
- Use: Watch Online & Download
- Access Period: Unrestricted
- Download: MP4 (iPod compatible)
- Size: 125 MB
- Posted: 07/01/2009
This lesson is part of the following series:
This lesson was selected from a broader, comprehensive course, Physics I. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/physics. The full course covers kinematics, dynamics, energy, momentum, the physics of extended objects, gravity, fluids, relativity, oscillatory motion, waves, and more. The course features two renowned professors: Steven Pollock, an associate professor of Physics at he University of Colorado at Boulder and Ephraim Fischbach, a professor of physics at Purdue University.
Steven Pollock earned a Bachelor of Science in physics from the Massachusetts Institute of Technology and a Ph.D. from Stanford University. Prof. Pollock wears two research hats: he studies theoretical nuclear physics, and does physics education research. Currently, his research activities focus on questions of replication and sustainability of reformed teaching techniques in (very) large introductory courses. He received an Alfred P. Sloan Research Fellowship in 1994 and a Boulder Faculty Assembly (CU campus-wide) Teaching Excellence Award in 1998. He is the author of two Teaching Company video courses: “Particle Physics for Non-Physicists: a Tour of the Microcosmos” and “The Great Ideas of Classical Physics”. Prof. Pollock regularly gives public presentations in which he brings physics alive at conferences, seminars, colloquia, and for community audiences.
Ephraim Fischbach earned a B.A. in physics from Columbia University and a Ph.D. from the University of Pennsylvania. In Thinkwell Physics I, he delivers the "Physics in Action" video lectures and demonstrates numerous laboratory techniques and real-world applications. As part of his mission to encourage an interest in physics wherever he goes, Prof. Fischbach coordinates Physics on the Road, an Outreach/Funfest program. He is the author or coauthor of more than 180 publications including a recent book, “The Search for Non-Newtonian Gravity”, and was made a Fellow of the American Physical Society in 2001. He also serves as a referee for a number of journals including “Physical Review” and “Physical Review Letters”.
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A sound wave refers to a longitudinal wave propagating through some medium, although we usually reserve the words "sound waves" to talk about longitudinal waves or pressure waves in air, just what you think sound should be. So when I'm speaking or playing an instrument or making any kind of a sound, what's going on physically? Well, I am pushing on the air with some device and so I'm compressing the air a little bit. There are high-pressure regions. It's over-pressure. Of course, there's atmospheric pressure all the time everywhere, so I'm creating an over-pressure. And that means that the air molecules here are pushing against the air molecules in front of them, which get compressed, which push on the air molecules in front of them, which get compressed. So this is the way a pressure wave propagates through air, and that's exactly what any wave is. And this is a longitudinal wave. If you think about it microscopically, air molecules are being pushed forward by the high-pressure, and then they are pushing on the next molecules. So the air molecules are jiggling around--and forgetting about their random thermal motion--the motion of this wave is in this direction, and the motion of the molecules is in the same direction. So again, it's a longitudinal wave.
Just look at the longitudinal wave in this Slinky. I make a pulse and you can see a longitudinal pressure wave traveling down. What exactly is going on? At any moment in time there's some compression here. It's a good model for what's going on in the air except that this is just one-dimensional. And so what's happening is the Slinky is compressed here so it's pushing in front of it. So the compression wave is traveling downward. And there are really two waves, two different waves. They're equivalent but they feel different to think about longitudinal traveling waves. I'm thinking about this high-pressure region. You'll notice I can make a continuous pressure wave and you see what's happening. You get high pressure that's traveling, and behind it there is actually low pressure, under-pressure, because here it's been squished and behind it it's expanded, and then the next squish. So you get high pressure, low pressure, high pressure, low pressure, traveling along. So that's one way of thinking about a longitudinal wave, is in terms of pressure, over- and under-pressure.
Another equivalent way is to think about the motion of an individual piece of Slinky. Remember, the Slinky isn't moving that way in any sort of overall sense. The Slinky isn't getting thinner over here and thicker over there. If you watch this continuous wave traveling, it's a little bit complicated but if you think about it, this little piece of Slinky is moving over to the high-pressure region and then moving back. So this little piece of Slinky is just oscillating back and forth around its equilibrium position. And so just like a transverse wave where a little element of the medium is undergoing simple harmonic motion, so is that little element of the medium--here the metal in air, it's the little molecules--is undergoing simple harmonic motion back and forth around its equilibrium position.
So mathematically if we want to describe a sound wave, it's really quite easy. It's just analogous to transverse waves except instead of the displacement being in the perpendicular direction, this displacement f is the displacement of the molecule from where it would naturally want to be. It's a cosine function just like before. It's got an amplitude, which I'm calling fmax. So that's telling you how far off to the side this molecule is wiggling back and forth. And it just has the mathematical form of a good old traveling wave. This minus sign means this wave is traveling to the right. And so all the sort of mathematics that we've thought about for transverse waves you can really use because the math is the same.
And if you prefer to think about pressure waves instead of displacement, it's again that the pressure wave is just traveling along. It's a sinusoidal wave with some maximum over-pressure. I'm writing this as p. That's the difference of the absolute pressure from atmospheric. It can go to over-pressure or under-pressure as this sign goes from +1 to -1. And notice that this is a cosine and that's a sine. It's an interesting thing and worth thinking about. When the pressure is the highest, you're right in the middle of this compression. That's the spot where a little piece of Slinky is actually at its equilibrium. The pieces off to the side have displaced, compressing from both sides, but the one in the middle of the high-pressure region has f=0, and that's why one is a cosine and one is a sine. When one is maximum, the other one is at zero and vice-versa, so they're out of sync with one another.
p is related to fmax. I won't derive this but the maximum over-pressure is given by--this is the speed of the sound wave--the density of the air and the frequency of the wave. So the over-pressure depends on the frequency. If you make a high-frequency sound, there will be--all other things being equal--more over-pressure. And then it's proportional to the maximum amplitude of displacement of the air molecules.
So this is the mathematics, the physics of sound waves, and we're all set to talk about any physics quantities we might be interested in, like the energy being transmitted per second by sound waves and so on. You know, there's a human aspect of sound, which is really very interesting. It's what makes this physics especially compelling. When sound waves strike your ear, that's physics. But then there's this perception, and the perceptions that you have are all related directly to the physics. For instance, the frequency of the pressure wave that tells you the frequency of oscillations of your eardrums, and you perceive that as pitch. So you could have a low pitch; that's a low frequency sound, and high pitches are high frequency sounds. There is a connection between what you perceive and the physical equations.
There are other connections. For instance, what you perceive of as loudness comes out of these formulas. Loudness has something directly to do with the energy being transmitted into your ear per second per square meter, so that's a connection which is interesting to think about. Let's talk a little bit more about human perception of sound. You can hear sound waves in a range from about 20 hertz to about 20,000 hertz. That's for sort of a normal, healthy human ear. As you get older, especially on the upper end, you begin not to be able to perceive those high frequency sounds. Young people can hear high frequencies better. The more loud music you've listened to as a kid, the more you're going to degrade that high frequency end of your hearing, most likely.
There are sounds with frequencies below 20 hertz; you just can't hear them. There are sounds with frequencies above 20,000 hertz. Bats can hear higher frequency sounds. The doctor has a device, an ultrasound device--ultra sound refers to sound waves with frequencies higher than 20,000 hertz. Ultrasound typically might be 1 million hertz, so the corresponding wavelength is very, very small. It might be a millimeter or a fraction of a millimeter. And you can use those sound waves. When they hit a human body they'll act like waves and reflect and transmit, and you can make images using sound waves. It's kind of a neat application of sound waves.
I've talked about the velocity of sound, the speed of sound, but I haven't told you what it is. We had a formula for the speed of a transverse wave on a string. I'm not going to work out the formula for the speed of sound in air, but I'll just tell you the answer. It's about 331 meters per second. Now this is approximate. It depends on the local density of air. This is sort of standard density and standard temperature. There is an important and interesting temperature dependence. As the room gets warmer, sound travels a little bit faster. This has a big influence on musical instruments. You want to warm them up. So the approximate dependence--this is definitely a crude formula--is 331 meters per second plus 0.6 times temperature in degree Celsius. So at zero degrees Celsius, it's about 331 meters per second. At room temperature, 20 degree Celsius or so, you multiply that by 0.6. It's not a very big correction. So you can use 331 for most purposes.
And remember, it's a constant. So if you're producing a sound wave by wiggling your vocal chord with some frequency f, remember for any wave, times f is going to equal to the speed of that wave. So you don't get to independently choose the wavelength of the sound and the frequency. Once you've picked one, this formula determines the other. So if you're making a vibration at 440 hertz and you plug that into this equation, you'll get a wavelength which is a little but under a meter, and that's just what you get. That's the distance in space between one high pressure front and the next high pressure front, the wavelength of the sound pressure waves.
In fact, let's talk about that a little bit more because this is an important difference between sound waves and the kind of transverse waves on a string we've been talking about, or longitudinal waves on a Slinky. Those are one-dimensional. And sound waves are three-dimensional. When I'm speaking, I'm creating a pressure wave, which goes out in all directions. If you look down on it and get a two-dimensional view, here's the sound being generated. And what am I drawing here? These are called wave fronts. This might represent, for instance, a region of high pressure, and then the white might be low pressure; high-pressure, low pressure, high pressure, low pressure. And these are traveling outwards, and so you get these expanding spherical waves of pressure and they're traveling outwards at the speed of sound, about 331 meters per second.
When you think about this in three dimensions, you can see that something interesting happens with the power being transmitted because the energy is being spread out, and so that's an interesting thing that we really need to talk about in a future tutorial. What happens to the loudness or intensity as you get further away? In fact, there's lots of interesting physics to think about with sound and the connection to human perceptions. Here I've got these mathematical formulas. I can work with them; I can figure out all the physics properties of sound. But listen to an oboe playing Concert A, 440 hertz, and a violin playing Concert A. Same frequency; it sure sounds different to me. Can I connect that sensation of what's different to the physics, the mathematics? How does that show up in these equations?
Similarly, I was just talking about intensity. That's a technical work, which I haven't defined carefully yet--and we will. It has to do with energy per second per square meter. That's the physics. How does that connect with my perception of loudness? Interesting stuff.
Sound Waves Page [3 of 3]
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