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Acoustics Final Exam     due at noon on Wednesday, September 29, 2004

You may consult only your textbook, your notes, your calculators, and me. Be sure to explain your answers thoroughly and clearly. This includes showing any calculations you may make. The correct answer with the wrong explanation, or no explanation, is worth no credit. Any typos I notice, or changes of heart I have, will be posted on the web page. When you've finished a problem, read it over carefully; cross out what you no longer believe, and draw a box or circle around the final answer. When you've finished, sign the honor code, staple these pages to the front of your papers, and turn it in (slide it under my door if I'm not here.). If you have any doubt about what I mean or what I want, please ask me about it.

•  David told us that the different modes on a Chladni plate do not have frequencies that are integer multiples of some fundamental frequency, that is, the plate doesn't have harmonics. Mike reported that the koto also did not produce harmonics. Why was this latter fact surprising, whereas the plate's lack of harmonics was not?

•  The lowest note on a piano is A0 (27.5 Hz). The string (actually the "strings" are wires.) is perhaps 84 inches long. What is the speed of wave propagation on this string? What is the wavelength of this fundamental frequency in the air? On the string?

•  A bassoon is about 9 feet long and a clarinet is 635 mm long. The lowest note on the bassoon is the B-flat two octaves below middle C, while the lowest note on the clarinet is the E below middle C. Do the appropriate calculations to show that this does or does not make sense. (One inch is 2.54 cm, 1 cm is 10 mm. I am not going to tell you how many inches are in a foot.)

•  It has been said that two voices singing a fifth apart is a "boring" harmony - it's too consonant. Compare this harmony with two voices singing a fourth or a major third apart, showing why the fifth is boring.

•  Give explicit directions for playing the fifth harmonic on a guitar string; we want the tone to be as pure as possible. If this is played on the low E string, what note results?

•  Two speakers are connected to the same sine-wave generator. At one location (perhaps your ear) speaker A alone creates sound of intensity 1 microwatt per meter-squared. Speaker B alone creates sound of the same intensity. Now, if both speakers are on, the sound intensity could be different. What is the minimum intensity at this location, and what are the circumstances that could cause that to happen? . What is the maximum intensity at this location, and what are the circumstances that could cause that to happen? Could the resulting intensity be 2 microwatts per meter-squared? If it's possible for the intensity to be different from that, where did the extra energy come from, or where did the missing energy go?

•  Suppose you hold down the sustain pedal on the piano, so none of the strings are damped, and you pluck the string for middle C. Of the strings within one octave of middle C, which will vibrate in response to this, and why?

•  Suppose I get out the headpiece of the flute and play a note, the fundamental pitch. Let's call this frequency f 1 . I can overblow to get other notes; what are their frequencies, in terms of f 1 ? I can then close off the end of the flute with my hand. In terms of f 1 , what notes can I get?

•  You're listening to music from a speaker that's 10 feet away from you, and the sound level is 80 dB. Now a second speaker, 20 feet from you, is turned on. With both speakers on, what is the new sound level?

•  We found, with those two bars tuned to 440 Hz and to 441 Hz, that many people can't hear the difference between these two frequencies. Suppose two flutists are playing a duet, and at one point are playing concert A in unison. However, while one flute is producing a perfect A (440 Hz), the other is just a tiny bit flat and is actually producing a frequency of 439 Hz. For those who cannot distinguish between two such similar pitches, are there any consequences of this flatness, and if so, what are they?