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course Phy 202
Problem Number 1
A string of length 8 meters is fixed at both ends. It oscillates in its third harmonic with a frequency of 199 Hz and amplitude .31 cm. If it is held under a tension of 9 Newtons, then what is its mass?
**** I am having trouble with this one for some reason, could you help me with an equation? do I use this equation? v = sqrt( T / (mass/unitLength) )
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The formula relates T, mass per unit length and propagation velocity v.
The problem gives you T.
To find the mass you also need the propagation velocity.
You get this by the fact that the string oscillates in the third harmonic at 199 Hz.
What is the node-antinode structure of the third harmonic?
How far is it between a node and an antinode?
What therefore is the wavelength?
What given quantity do you combine with the wavelength to find the propagation velocity?
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****
Problem Number 3
If a traveling wave has wavelength 2.7 meters and the period of a cycle of the wave is .071 second, what is the propagation velocity of the wave? What is its frequency?
Period = lambda/ v v = lambda/period = 2.7 m / .071 sec = 38 m/s Freq. = v / lambda 38 m/s / 2.7 m = 14 Hz
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Good.
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Problem Number 4
A sound source with frequency 130 Hz approaches an observer at 95 m/s. If the speed of sound is 340 m/s, then what frequency will be heard by the observer?
fl=((v+vl)/v)*fs=((340+95)/340)*130
=166.3 Hz
Problem Number 5
The SHM of the left-hand end of a long string is given by y = .59 cm * sin ( ( 7 `pi rad/s) t ). This motion induces a traveling wave in the string. The string has tension 19 Newtons and mass per unit length is 12 grams / meter. Explain how we know there is energy in the wave, and find how much energy there is in 11.4 meters of this wave.
a=fnf(.5,2,.01) b=fnf(3,9,1) c=fnf(5,50,2) d=fnf(3,19,1) e=fnf(3,20,.1)
f=fnf(.03,.09,.001)
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Note that this is an introductory problem set problem.
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Sound is created by the vibration of the air column in a pipe which is open at both ends. The pipe is 5.9 meters long, and the speed of sound is 348 m/s. What are the frequencies of the first four natural harmonics? What are the successive frequency ratios (i.e., the ratio of each but the first frequency to the next lower frequency), and how well can each be approximated by a power of 2^(1/12)?
1st natural harmonic- 2L = 5.9 *2 = 11.8 m
348 m/s / 11.8 m = 29.5 Hz
2nd - 3/2 L = 5.9 m * 3/2 = 8.9 m
348 m/s / 8.9 m = 39.1 Hz
3rd - 4/3 L = 5.9 * 4/3 = 7.9
348 m/s / 7.9 m = 44.1 Hz
4th - 5/4 L = 5.9 * 5/4 = 7.4 m
348 m/s / 7.4 m = 47 Hz
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Between the antinodes at the two ends the pipe can contain 1, 2, 3, ... nodes; an antinode has to occur between each pair of nodes.
If the configuration is A N A then the length of the pipe is 1/2 wavelength.
If the configuration is A N A N A then the length of the pipe is 1 wavelength.
If the configuration is A N A N A N A then the length of the pipe is 3/2 of a wavelength.
etc..
You know the length of the pipe, so you can find the wavelengths of the various harmonics.
Whatever formulas you are using don't match the situation. Reason it out as indicated here.
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Problem Number 2
What is the angle of total internal reflection from a material which has index of refraction 1.6 to a material with index of refraction 1.03?
I am having trouble with this problem. I do not see a given angle degree so I am having trouble. I looked at the intro problem set and the problem had a degree and 2 index of refraction.
Do I use Snell's Law?
arc[sin(DEGREE)*1.6/1.03]= DEGREE
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The angle of total internal reflection is an angle, which is determined by the two indices of refraction.
It would be the angle such that the angle of refraction is 90 degrees.
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Problem 4
Find the frequencies of the first four harmonics of a standing sound wave in an open pipe of length 3 meters and in which sound propagates at 340 m/s.
freq=v/length
1st: f=340 m/s / ***would you divide it by 3m and then 3/4, 4/3,5/2? ****
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Reason this out as in the similar problem above.
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Check my notes. You're welcome to submit revisions and/or questions in the form of a copy of this document, and insertions marked with &&&&.
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