Phy 122
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Mr. Smith,
I am working on a practice final that has the following questions on it. I don't understand how to do the second and third ones, but the first I need clarification on how to solve this with two different ohm values. This question was on my exam 4 and I didn't know exactly how to do it. Can you please explain how to solve the following problems so I can do them if they end up on my final?
Thank you.
1. A circuit has a source that creates a constant 3 Volt potential difference across parallel resistances of 44 Ohms and 47 Ohms. What is the current through the source, and how much power is dissipated in the first, and in the second, resistor?
2.Our musical scale is based on the natural harmonics of strings and air columns. We use a scale consisting of a sequence of pitches each of which hass 2^(1/12) the frequency of its predecessor. On the piano keyboard, for example, the frequency ratio of any white or black key to the key just before it (whether white or black) is 2^(1/12). The approximate value of this ratio is 1.0594.
Show that if we start at any key and count up 7 keys we will achieve a ratio of pitches very nearly equal to 3/2 (this ratio is called a 'fifth', corresponding to a span of 5 white keys on the piano).
Show that if we start at any key and count up 12 keys we will achieve a pitch ratio of 2/1 (this ratio is called an 'octave', corresponding to a span of 8 white keys on the piano).
Determine how many keys we must count up from a given key to come as close as possible to the ratios 4/3 (called a 'fourth', corresponding to a span of 4 white keys on the piano), 5/4 (called a 'third', corresponding to a span of 3 white keys on the piano), and 6/5 (called a 'minor third', corresponding to a span of 2 white keys and a black key on the piano). Musicians will note that these ratios are of primary importance in Western music.
How close do the ratios based on the ratio 2^(1/12) come to mimicking the natural ratios of the harmonics of a string?
If 12 divisions of 2 come this close, it seems like a greater number of divisions, for example 26, might do an even better job. Use your calculator to find the ratio that would correspond to 26 subdivisions, and determine how nearly the natural ratios could be mimicked using multiples of this ratio.
It turns out that the next number of divisions that actually improves on 12 is 43. This ratio is used in some Eastern music. How much better can we do with a division of the ratio 2 into 43 equal subdivisions, as compared to 12 subdivisions?
This problem is solved in the Introductory Problem Sets, Set 6. I believe it is Problem 14.
Note that your test is generated from the Introductory Problem Sets.
3.
If an electron can orbit a proton only in orbits having angular momentum h/(2`pi), 2 * h/(2`pi), 3 * h/(2`pi), ... , n * h/(2`pi), ..., then what is the radius of the closest possible orbit? How many deBroglie wavelengths are required to span the circumference of this orbit? What are the radii of the two next-closest orbits? What is the radius of the nth-closest orbit? What it is the total energy of each of these orbits? How many deBroglie wavelengths are required to span the circumference of each orbit?
Problems 7 - 11 in Introductory Problem Set 7 are relevant to this situation. I believe it is Problem 8 that addresses the specifics of this question.
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I listed the practice final exam problems above that I need clarification and help solving. Thanks.
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I'll be glad to answer any questions you have related to the solutions given in the Introductory Problem Sets. The questions you ask about are both taken directly from Introductory Problem Sets, and I've given you references to the appropriate sets and, I believe, to the specific problems.
If there's anything you don't understand in those solutions, be sure to let me know so I can clarify.
Note that if you have completed the four tests, the exam is optional. A good exam could cut you a little slack with the labs, or could of course raise your test average. It can't lower your average.