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practice final solutions

practice final solutions - Physics 1C Summer Session I 2011...

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Physics 1C, Summer Session I, 2011 Final Exam Instructions: Do any 8 problems. Please do all work on separate sheets of paper, and hand in everything you want to be graded. Clearly mark the problems that you want graded, and box the answers. 1. A mass on a spring undergoes simple harmonic motion. The speed of the mass is given by the following expression: (a) What is the frequency of the mass's motion? (b) What is the total energy of the harmonic oscillator? Solution: (a) The angular frequency is 12.6s -1 , so the frequency is 12.6s -1 / 2 π = 2.01s -1 . (b) The total energy is equal to the kinetic energy when the speed is at its maximum value, since the potential energy there is zero. The maximum speed is 0.35m/s. Thus , E = 1/2 Mv 2 MAX = (0.0613m 2 /s 2 ) M . Due to a typo, the mass M is missing from the problem statement; it's supposed to be 0.10 kg . It's OK to just leave it as M , and if this mistake was discovered during the actual final, we would just announce a correction and write the value of M on the board. 2. A string with a mass per unit length of 0.050 kg/m is tied down at both ends, 1 meter apart, and held under tension. The fundamental frequency of the string is 120 hz . (a) What is the 5th harmonic frequency? (b) What would be the fundamental frequency if the tension was doubled? Solution: (a) The 5th harmonic frequency is just 5 times the fundamental, so it is 600 hz . (b) The fundamental frequency is proportional to the square root of the tension, so increasing the tension by a factor of 2 would increase it by a factor of sqrt(2). The new fundamental frequency would be 120 sqrt(2) = 170 hz .
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3. A jet aircraft flying 300 meters overhead produces a sound intensity level of 110 decibels on the ground. What is the total power produced in sound waves, in watts? (a)
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