Physics 1240 Hall Chapter 3 Notes 1

Focus questions and learning goals

Chapter 3 focus questions: 1. How can we make sound? 2. What are the physical differences between different ways of making sound? Chapter 3 learning goals. After studying this chapter, you should be able to: 1. Predict how the sound of various instruments—particularly string and wind instruments—will change as you: (a) Make the instrument longer. (b) Tighten the instrument’s strings. (c) Strike, pluck or blow harder on the instrument. 2. Explain how you could change the pitch of an instrument by precisely an octave. 3. Explain what’s so special to humans (and music) about an octave. 4. Explain why some percussion instruments tend not to have well defined pitch, but do have a sort of “rough pitch.” 5. Predict how that pitch depends on the size of the instrument. Explain what else might affect the pitch besides size. 6. Design a drum whose pitch you can change. 7. Explain why electric guitars are so quiet if they’re not plugged in.

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Sound categories

This chapter focuses on the production of sound (as opposed to propagation and perception). It’s the first introduction in this course to broad categories of instruments. This chapter is fairly qualitative and descriptive. The discussion has some useful concepts and vocabulary, and sets us up for more detailed study of instruments in a few chapters. Note that we’re not looking to “zoom in” just yet! In the first section of the chapter, Hall tries to categorize sounds. This has some value, although frankly I think that for whatever categories you come up with, we can find interesting sounds that don’t fit exactly in the categories. The first distinction is natural versus artificial. We’re going to be mostly studying artificial sounds: this means sounds produced on purpose, by us, for some reason, generally musical. (Although artificial sounds could be produced for medical or other research reasons.) So, if Laurie Anderson records a buzzing bee and plays it in a concert, is that natural or artificial? What if she slows it down or distorts it to make sound cooler? 1

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Then there’s original versus reproduced. This has little to do with the sound itself, although we’ll certainly be interested in the fidelity (honesty, faithfulness) of recorded sounds. This will come much later in the course! The author then introduces steady versus transient sounds. A steady sound is one that is close to periodic: it continues in the same way for many cycles. Unlike the sinusoidal waves shown in the book and in class, real waveforms are never perfectly periodic. Therefore all sounds are transient to some extent. Real waveforms start (“attack”) and end (“decay”). The amplitude may be fairly constant while the sound is playing, or it may vary, fade, rise and fall. Last chapter when we looked at waveforms, we started talking about issues of transience. If you look at figure 3.1 of the text, you see a note which is transient (it dies away after only about a dozen cycles), yet it does have a characteristic period. The period is the time for one wiggle to occur, not for the whole transient to die away. In figure 3.1, the period looks like it is about 0.5 msec, which means a frequency = 1/Period = 2000 Hz = 2 kHz. So you’ll percieve a note of 2000 Hz, which lasts for about 5 ms. This would sound like a “high click”. (Does this make sense? Ask if you don’t get it!) Web demonstration: You can make sounds of different frequencies and different durations using the interactive visual sound applet. Go to the webpage in this footnote1 , or see the link to this simulation from the course web page (click on “Interactive visual sound applet” under “Resources”). In this applet, the horizontal axis is the time the sound is played, and the vertical axis is the pitch of the sound. By “coloring” different pixels in the applet, you can make different frequencies play at different times. Experiment with different durations by drawing horizontal lines (constant pitch tones) of different lengths. Of course all sounds are ultimately transient, but some are more transient than others! Think of the difference between saying the letter “P” and saying the letter “E” while holding it. The former is definitely transient, while the latter can be quite steady (for awhile!) Thinking about this raises all sorts of interesting questions. How do we feed energy into these two letters? How do we sustain the “E”? This is something we’ll want to talk about, to make sense of instruments and distinguish, for example, percussion from wind instruments. Percussive “notes” tend to be more transient, while wind notes can be quite steady.

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Instrument categories

Thinking about different types of sounds leads us pretty naturally to considering “families” of musical instruments. Again, how we define the categories can be quite arbitrary. Since this is a physics class, we’ll try to look at categories that have powerful, physical commonalities. For example, wind versus string instruments is a distinction we can easily justify based on the physics. But even then, a flute is quite different from an oboe in the physics involved. For now, we’ll do a quick survey of percussion, wind, and string instruments, and come back to all of them later in more detail. But remember that the categories aren’t absolute: does a piano count as percussion or string?

3.1

Percussion instruments

Remember that all sounds arise from pressure waves in the air. If an object is vibrating with some frequency f , the object will push back and forth on the air, making a sound with that frequency. 1

http://www.seeingwithsound.com/javoice.htm

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If you whack a solid object, generally you put some energy into it, and it starts to vibrate. The object may have one natural resonant frequency, but in reality, all real objects have multiple possible vibrations. You will generally excite vibrations with lots of different frequencies when you whack the object. Waves (disturbances) will travel back and forth across the object. If the object is solid, they might travel through it, or they might be wiggles of the surface. For a drumhead, a whack will generally make a surface vibration, which means a disturbance of the surface that travels out in 2 dimensions, bounces off edges, passes through itself, and ultimately decays away. See Fig 3.2 of the text for an illustration of this. Large amplitude vibrations, as we’ve seen before, tend to move more air (make bigger pressure amplitudes), and thus sound louder. The more efficiently you can couple the wiggling surface to the air, the louder and clearer the sound will be. If the size of the wiggling object is small, you generally won’t get much sound out: bigger surfaces move more air around and therefore usually make louder sounds. 3.1.1

Friction and duration

All objects have internal friction, which makes their vibrations die away. You can design instruments to vibrate for a long time (like the Tibetan singing bell) or for a short time (like a xylophone bar). It’s a question of how efficiently you dissipate the vibrational energy into heat (or into other objects like the table or floor the instrument sits on) No bell can ring forever, because the sound waves themselves carry away some of the stored energy! Tuning forks vibrate for a long time and are very quiet. You have to hold a tuning fork right to your ear to hear it. They have relatively little losses (relatively low internal friction), and have very well defined resonant frequencies. If you want to hear a tuning fork more easily, you need to put it onto a bigger surface which can vibrate, and couple to the air better (a box works well). This setup makes the sound louder, but it also means the sound becomes more transient—the sound dies away faster, because you’re losing lots more energy to the produced sound! Home experiment: Find or make an instrument, vary its coupling to other objects, and see what happens to the duration of the sound. You could use a drum. But if you don’t have access to a drum, try making a sound with anything you can whack and make a noise: it could be a ruler, a metal rod, a piece of silverware or a glass, a guitar string, or something else. After whacking your “instrument” a few times to see how long the sound lasts, do something to change the coupling. The easiest way to do this is to touch your instrument with a relatively soft object, like your hand. (Vibrations dissipate, or decay, more quickly, in soft, easily deformable objects.) How does the sound duration change with this additional coupling? 3.1.2

Pitch of percussion instruments

Drums usually don’t have a very clear pitch, although when you hear a drum you will have a rough sense of “high” or “low”. Why is this—what makes drums different from other instruments we’ll talk about? There are a couple reasons. First (and most important), the shorter a sound lasts, the less well-defined the period is. You can think of this as an interpretation problem: when you don’t have a lot of cycles, it’s hard to measure the period, so there’s a sort of mixup in interpretation between the time for a cycle, and the time that the whole disturbance lasts. Second, complex surfaces like drums can produce more than one frequency at the same time. (This is pretty crazy and different from the vibration of simpler objects like tubes and strings, and is worth thinking 3

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about!) But the shortness of the sound really dominates the story. Imagine that you record a perfect sine wave, and play it back. If you only play one or two cycles (which might last only a tiny fraction of a second), you hear a little “click”, and it’s very hard to say what tone it is. There’s some mathematics behind this as well as just perception issues. We’ll come back soon and talk about why this is—it’s related to what makes the color, quality, or timbre of notes. Whether an object sounds high or low is determined by a bunch of things, all of which lead to the resonant frequencies of the object. For a mass on a spring, we learned that the natural frequency gets higher if the object (spring) is stiffer. We also learned the frequency gets higher if the object has less inertia (or mass). An object is easier to move around if it has less inertia! But size comes into play too—a very long object is likely to be floppier, and have lower frequency. A different way to think about this is to argue that a disturbance takes a longer time to make the trip to the end and back (then reinforcing itself), and longer round-trip time means lower frequency. The book categorizes percussion instruments into membranophones (like a drum with a stretched membrane head), metallophones (like a bell or chime), actually made of a long vibrating piece of metal, and xylophones (vibrating wooden objects). Clearly there are more: What if the vibrating material is plastic? What is the category of a piano? By increasing the tension of a membrane, you make it stiffer, and raise the pitch. Adding resonating chambers connected to the vibrating object can resonate one (or a few) frequencies more strongly, making the pitch better defined (and dependent on the size and shape of the chamber)

3.2

String instruments

Strings are sort of a type of percussion instrument: think of a metallophone made of a thin stretched metal string! But it’s useful to separate string instruments out from other percussion instruments because of a key property of strings. This key property is: when plucked, there are only a few very definite, sharp frequencies that will tend to resonate. Even if you whack a string, it will vibrate at its preferred frequency. That frequency is determined by the tension (higher tension leads to higher tones), by the inertia (heavier strings lead to lower tones), and by the length (longer strings lead to lower tones). Can you begin to see why these properties occur? It’s all the same physics we’ve been talking about! Because of the well-defined resonances of strings, string instruments have clearer tones of longer duration than do percussion instruments. Another very important property of strings is that we can control the tones! For example, if you put your finger on the string somewhere and make it shorter, you make the pitch go up. (By pressing down on the string at some spot, you are “pinning down” the string at that point—it can’t move where it’s pinned, just like the string is pinned at the end.) The frets on a guitar guide your fingers to spots that make nice, well defined notes. (And, the fret is something rigid to push against, to hold the string down at that spot). Some instruments have no frets (for example, the violin, viola, and cello) so you need some more skill to know where to push! You can fine tune the pitch by increasing or decreasing the tension; this is why most string instruments have tuning pegs to tighten them. Home experiment: Find a string instrument to play with. (If you don’t have one, see if a friend or neighbor will show you hers: you could do this with a guitar, bass, banjo, violin, viola, cello, or even a ukelele.) Pluck the strings and listen to the sound. Can you see which strings are thicker and more massive? How does the pitch vary with the thickness of the string? Experiment with pressing down on the strings: can you make the pitch of a given string higher and higher by moving your finger farther down the neck? How high can you make the 4

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pitch? Can you change the pitch by exactly an octave? (Read the section on octaves below if you don’t yet know what that means.) If the instrument’s owner is okay with you de-tuning the instrument, try changing the tension of the strings. Which way do you have to turn the tuning pegs to make the tension higher or lower? What happens to the pitch when you do this? How big an adjustment is necessary to hear a different pitch? Finally, try plucking the string at different places along its length. What happens to the sound? Can you explain why? 3.2.1

Sounding boards

Here’s a confusing but important fact about string instruments: a wiggling string does not move much air. In fact, you can barely hear a vibrating string! When you play a guitar, a violin, or any string instrument, it is not the vibrating string that generates most of the sound you hear. Is that surprising? Think about it. Because it’s so thin, the string doesn’t make much of a pressure wave in air; instead, it “slices through” the air with little effect. So how do we hear string instruments? You always need some sort of device to connect the vibrating string to a much larger surface (like the back of the violin, or the back of the guitar). It’s the bridge, which the strings stretch across, that brings the vibration from the string and carries it to the body. The moving air that is the start of the pressure wave is being moved by the body, not the string. If you take the back off a violin, it becomes nearly silent! Indeed, electric guitars are designed not to transmit the string vibration to the body. Even though an electric guitar looks like an acoustic guitar, if the electric guitar is not electronically amplified, you can barely hear it. (And the strings may even be bigger and thicker than on an acoustic guitar!) If you know someone who owns an electric guitar, try playing with it unamplified and see what happens. One of the key physics questions about string instruments is this: how do you get them to vibrate, and how do you get them to keep vibrating so you hear a steady tone? We’ll come back to this—bowing, strumming, and plucking all can work in different ways.

3.3

Octaves

Important concept: If you make an object vibrate exactly twice as fast (double the frequency), you get a new tone which your ear closely identifies with the first. We give the notes the same name (for example, “A” can be a low A, or a high A. They differ by one having exactly double the frequency of the other). The notes sound like they “fit”, and the vibrations of your eardrum match up closely, because every second wiggle of the higher one lines up with every wiggle of the lower one. This is called an octave. String instruments make it really easy to see and hear what an octave is. If you double the length of a string, it takes twice as long for a vibration to make it down and back, so it wiggles at half the frequency, or one octave lower. If you put your finger in the middle of a string, making it half as long, it wiggles twice as fast, moving the tone up by an octave. We’ll investigate this much more soon, but hopefully it makes some sense now. In general, doubling the length of an instrument makes it lower by an octave (although it can certainly be more complicated than that, since you might also change other things like tension or inertia too when it gets bigger). String instruments create vibrations whose frequency is determined by the stiffness, mass, tension, and length of the string. For a given string, shortening the length by a factor of 2 will increase the pitch by one octave (doubling the frequency, see below). The connection between frequency and wavelength, v = f λ, still holds. Here, λ (the wavelength) has to “fit” evenly along the string (the string must be one, or two, three, or so on half-wavelengths long). The speed is the speed 5

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of a wave on a string, which arises from the tension and weight. So the speed is not the speed of sound in air, it’s the speed of the wave on the string that determines the frequency that the string vibrates at for a given length.

3.4

Wind instruments

Wind instruments work quite differently from strings. To make a wind instrument, you build some sort of resonating chamber where the air itself can vibrate. The resonant frequency or frequencies will be determined largely by how big the chamber is (and its shape). As with other instruments we’ve discussed, larger chambers make lower frequencies (more time is needed for vibrations to get back to where they started). Lots of wind instruments have resonating chambers that are tubes: for example, organs, recorders, clarinets. To play tunes made up of different notes, you need to control the size of the resonating chamber. You might do this by opening or closing holes along the tube, which changes how the air can vibrate inside the tube and effectively changes the tube’s length, or you might do this by switching to longer/bigger pipes in an organ. Second, you need to generate and sustain a vibration in the chamber which can resonate! Different winds have different tricks to “feed energy” into the chamber and excite vibrations. Some just use the hissing of air running past a sharp edge (for example, the flute and recorder). This is called an edgetone. An edgetone is not what you hear when you’re playing, because the instrument itself is only resonating/amplifying some of the pitches. Some instruments use a reed, which is a little piece of material that flaps and buzzes when you blow air past it. You don’t have to put energy in at one frequency - you can put in lots of frequencies, and let the chamber “pick out” (resonate at) the frequencies it finds natural. That’s generally how it goes—if you blow on a mouthpiece of a wind instrument (a reed, a trumpet mouthpiece, a recorder mouthpiece only) you’ll hear a “buzz” or “hiss” because there are many frequencies all sounding on top of each other. The instrument then resonates and amplifies one frequency or a few frequencies. Home experiment: Find a wind instrument to play with. (If you don’t have one, see if a friend or neighbor will demonstrate his. The instrument could be a recorder, clarinet, oboe, flute, saxophone, trumpet, trombone or other horn, or something else.) Play the instrument and listen to the sound. What happens to the pitch when you alter the length of the tube, by opening/closing the holes (flute, recorder, saxophone, clarinet) or sliding the slider (trombone)? Does the pitch change in the way you would expect? Can you change the pitch by exactly an octave? Try changing the way that you blow into the instrument. What happens to the sound? Can you explain the change? The wind instruments are roughly grouped into three categories. The reed instruments include the oboe, saxophone, clarinet, and bassoon. They are harder to play than some other instruments, because you need some physical skill to make the reeds vibrate properly! The edgetone instruments include the flute, piccolo, recorder, and organs. The final group is the brass instruments, which use your mouth and lips as the “reed”. An amazing feature of brass instruments is that there is some feedback from the size/shape of the resonating cavity that makes your lips vibrate at the same frequency as you’re playing! The brass group includes the trumpet, trombone, french horn, and tuba. Your voice is a bit like the brass instruments, where your mouth becomes the resonating cavity! (If this doesn’t make a lot of sense, that’s ok. There will be more on this later in the course.) 6

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What determines the frequency of a wind instrument? In the discussion of string instruments above, I explained how the speed of sound in the string is important to determine the frequency. For a wind instrument, there is no string. Instead, it’s the air in the chamber that vibrates, and so now when we write v = f λ, the speed v really is the speed of sound. (Remember, this is 344 m/s at room temperature.) The size of the chamber determines the wavelength, and the frequency that you hear is then determined by this relation. You do not have control over the speed for these instruments, so your only “knob” is the allowed wavelengths. This is why size (and shape) of the instrument is so much more critical for winds. (Think of a guitar, with four equal length strings of very different pitches! Would it be possible to make four different wind instruments of the same length but very different pitches?)

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Summary

Let me wrap up by reminding you of the bottom line that you should take away from Chapter 3, and remind you of some questions you should be able to answer now. Percussion instruments make sounds of a short duration and made of a mix of many different frequencies. They do have some pitch, but usually don’t have such a well-defined tone as string and wind instruments. Can you name a few different percussion instruments? What can you do to a drum to make the sound higher or lower? String instruments take advantage of the well-defined resonant frequency of a vibrating string. The string itself doesn’t make much sound because it doesn’t move much air, so the resonant wood back of the instrument is needed for a loud sound. The pitch of the sound depends on the mass, tension, and length of the string. How can you take advantage of this dependence to play different musical notes? What do you need to do to the string to change its note by an octave? What effect does changing the tension in the string do? Wind instruments are all based on a resonating chamber in which air vibrates at a specific frequency. The fact that the chamber resonates means that you can excite the instrument at lots of different frequencies and the instrument will “pick” the right frequencies to make a nice-sounding note. What are some different wind instruments? What is the difference between edgetone and reed instruments? What is the effect on the pitch when the length of the instrument changes? What happens to the pitch if the air temperature changes?

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