Your
name:________________________________ honor code:
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 youÕve 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 youÕve finished, sign the honor code, staple
these pages to the front of your papers, and turn it in (slide it under my door
if IÕm not here.). If you have any doubt about what I mean or what I want, please ask me about it.
1) 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 doesnÕt have harmonics. Mike reported that the koto also did not produce harmonics. Why was this latter fact surprising, whereas the plateÕs lack of harmonics was not?
2) The lowest note on a piano is A0 (27.5 Hz). The string
(actually the ŅstringsÓ 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?
3) 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.)
4) It has been said that two voices singing a fifth apart
is a ŅboringÓ harmony Š itÕs too consonant. Compare this harmony with two
voices singing a fourth or a major third apart, showing why the fifth is
boring.
5) 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?
6) 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
itÕs possible for the intensity to be different from that, where did the extra
energy come from, or where did the missing energy go?
7) 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?
8) Suppose I get out the headpiece of the flute and play
a note, the fundamental pitch. LetÕs call this frequency f1. I can
overblow to get other notes; what are their frequencies, in terms of f1?
I can then close off the end of the flute with my hand. In terms of f1,
what notes can I get?
9) YouÕre listening to music from a speaker thatÕs 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?
10)
We found, with those two
bars tuned to 440 Hz and to 441 Hz, that many people canÕt 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?
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