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Lab 2 Resonances of Sound 2 Resonances of Sound Apparatus sound di↵erent from “A” on a saxophone is that the 880 Hz overtone would be quite strong for the sax- Oscilloscope . 1/group ophone, but almost entirely missing for the clarinet. Aluminum and Steel Rods . 1/group Although Helmholtz thought the relative strengths Tuning Fork Wooden Box w/ striker . 1/group of the overtones was the whole story when it came SCHURE-C606 Mic w/ BNC adapter . 1/group to musical timbre, actually it is more complex than that, which is why electronic synthesizers still do not sound as good as acoustic instruments. The timbre depends not just on the general strength of the over- Goals tones but on the details of how they first build up Find the speed of sound in air using a tuning (the attack) and how the various overtones fade in fork wooden box “pipe.” and out slightly as the note continues. Why do di↵erent instruments have di↵erent sound Measure the speeds of sound in steel and in spectra, and why, for instance, does a saxophone aluminum. have an overtone that the clarinet lacks? Many mu- sical instruments can be analyzed physically as tubes that have either two open ends, two closed ends, or Introduction one open end and one closed end. The overtones correspond to specific resonances of the air column In the womb, your first sensory experiences were of inside the tube. A complete treatment of the subject your mother’s voice, and soon after birth you learned is given in your textbook, but the basic principle is to distinguish the particular sounds of your parents’ that the resonant standing waves in the tube must voices from those of strangers. The human ear-brain have an antinode (point of maximum vibration) at system is amazingly sophisticated in its ability to any closed end of the tube, and a node (point of zero classify vowels and consonants, recognize people’s vibration) at any open end. voices, and analyze musical sound. Until the 19th- century investigations of Helmholtz, the whole pro- cess was completely mysterious. How could we so Setup easily tell a cello from a violin playing the same note? A radio station in Chicago has a weekly contest in Plug the microphone (with BNC adapter) into CH 1 which jazz fanatics are asked to identify instrumen- of the oscilloscope. You will be using the oscilloscope talists simply by their distinctly individual timbres to measure frequencies, but you’ll have to play with — how is this possible? the knobs to see a nice sine wave on the ’scope. The horizontal scale should be something like 1ms to see Helmholtz found (using incredibly primitive nonelec- the sound waves (once you see the wave you can tronic equipment) that part of the answer lay in the adjust the horizontal scale). relative strengths of the overtones. The psychologi- cal sensation of pitch is related to frequency, e.g., 440 Set the source to AC, and try to get a nice picture of Hz is the note “A.” But a saxophonist playing the a sound wave produced by the tuning fork / wooden note “A” is actually producing a rich spectrum of box (place the mic near the open end of the box). frequencies, including 440 Hz, 880 Hz, 1320 Hz, and Try to capture a screenshot as well, and measure a many other multiples of the lowest frequency, known frequency. as the fundamental. The ear-brain system perceives all these overtones as a single sound because they are all multiples of the fundamental frequency. (The Ja- Observations vanese orchestra called the gamelan sounds strange A Speed of Sound in Air to westerners partly because the various gongs and cymbals have overtones that are not integer multi- Measure the frequency of sound waves coming out ples of the fundamental.) of the box as accurately as you can with the oscil- loscope. Compare this with the value on the tuning One of the things that would make “A” on a clarinet 3 fork. Prelab Next, assuming that the sound wave that the micro- The point of the prelab questions is to make sure phone picks up is due to the fundamental frequency you understand what you’re doing, why you’re do- coming out of the box, find the wavelength of the ing it, and how to avoid some common mistakes. If sound waves. Note that the tuning fork box is closed you don’t know the answers, make sure to come to at one end and open at the other end. my office hours before lab and get help! Otherwise Using your measured values for λ and f,findthe you’re just setting yourself up for failure in lab. speed of sound waves in air. Compare with the value P1 For part A, you will measure the fundamental we’ve been using (343 m/s) and note the percent frequency of sound coming from the tuning fork box error. — call this f1. In terms of f1, what is the second- You probably got a value that is lower than 343 m/s lowest frequency of standing waves excited in the (if not, come tell me). Since we can measure the “pipe”? frequency pretty accurately, and since we know the P2 For part B, you will measure the lowest fre- actual speed of sound pretty well, what this is saying quency of sound coming from the metal rod such is that the actual wavelength is longer than what you that the middle of the rod is a node and the end of would expect (4L). This e↵ect is well-known, and so the rod is an antinode. If the length of the rod is L, people introduce an “end correction” to compensate what is the wavelength of this mode of vibration? for the fact that the sound reflections at the open end of the pipe are actually a little outside the pipe P3 For part B, the microphone picks up sound (see the Wikipedia articles on “Acoustic Resonance” waves in air, and yet the lab manual claims that you and “End correction” if you’re interested, but I got are actually measuring the speed of sound in metals. bored reading it pretty quickly). From the “Acoustic Explain why both of these things can be true, even Resonance” Wikipedia article, they suggest replac- though it seems contradictory. ing λ1 =4L with λ10 = 4(L + 0.4d), where d is the diameter of a pipe of circular cross-section. Calcu- late the speed of sound in air using this modified Analysis wavelength, using the width of your box as d.Do There is no formal lab writeup for this lab — make you get a value closer to 343 m/s? sure you answer all questions in the lab, and turn in your work at the end of the lab. B Speed of Sound in Metals The speed of sound in a solid is much faster than its speed in air. In this part of the lab, you will extract the speed of sound in aluminum and in steel from a measurement of the lowest resonant frequency of the metal rods. You will use the oscilloscope for an electronic measurement of the frequency, as in part A. For each of the two metal rods, do the following: Grab the rod with two fingers right at the middle, and hold it horizontally in the air. Hit one end of the rod (the wooden side of the mallet you have works well for this). Most of the sound comes the mode where there is a node at the center of the rod (where you’re holding it) and an antinode at the end of the rod. From measuring the frequency and inferring the wavelength (like we did in part A), you can find the speed of the sound waves. For this part of the lab, you do not need the correc- tion factor that you used in part A. Calculate the speed of sound in steel and in aluminum. Compare with values you find online. 4 Lab 2 Resonances of Sound.
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