Physics 221: Optical and Thermal Physics Exam 1, Sec. 500, 14 Feb Please fill in your Student ID number (UIN): IMPORTANT

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1 Physics 221: Optical and Thermal Physics Exam 1, Sec. 500, 14 Feb Instructor: Dr. George R. Welch, 415 Engineering-Physics, Print your name neatly: Last name: First name: Sign your name: Please fill in your Student ID number (UIN): IMPORTANT Read these directions carefully: There are 6 problems totalling 100 points. Check your exam to make sure you have all the pages. Work each problem on the page the problem is on. You may use the back. If you need extra pages, I have plenty up front. Indicate what you are doing! We cannot give full credit for merely writing down the answer. Neatness counts! I will give generous partial credit if I can tell that you are on the right track. This means you must be neat and organized. Each problem with its associated figure is self explanatory. If you must ask a question, then come to the front, being as discrete as possible so as not to disturb others. Put your name on each page it is asked for. You will lose credit if you fail to print your name on each page it is asked for.

2 Problem points. A block of mass M = kg is sliding without friction along a horizontal plane with velocity v = 1.00 m/s. The block encounters a spring of force constant k = N/m. Calculate how long it will take from the moment the block encounters the spring until it reaches the point maximum compression. k No friction v M If you work neatly I will find more partial credit for you!

3 Problem points. When you slosh the water back and forth in a tub at just the right frequency, the water alternately rises and falls at each end (high at one end and low at the other) while remaining relatively calm at the center. Suppose the time between successive maxima at one end is 1.5 seconds and the width of the tub is 0.75 meters. What is the speed of the water wave? Be neat. Neatness helps. Work neatly.

4 Problem points. The two wave pulses shown below are moving toward each other. The wave velocity is v = 1 m/s for both waves. The graph shows the value of the wave function y(x, t) at t = 0 : v =1 m/s y(x, 0) x (meters) v = m/s On the graph below, plot the behavior of the wave function at x = 0 as a function of time for the first two seconds after t = 0 : y(0, t) t (seconds) You must be neat. Neatness will count as part of the grade on this problem.

5 Problem 4. (20 points) One end of a string is attached to a wall and you pull the other end with tension T. Neglect gravity. Suppose that the rope can be driven by a small oscillator with frequency f. L f T Normally, the amplitude of the oscillator is so small that it has little effect, but if the frequency is right, a resonant standing wave will be excited in the rope. Suppose that when f = Hz the fundamental standing wave is excited. The length of the rope between the wall and the pulley is L = 1.00 m, and the tension in the rope is N. (a) Calculate the mass of the rope. (b) If the oscillator frequency f is left fixed at 100 Hz, what tension would be needed so that the first overtone standing wave is excited? You need to work Neatly! Don t forget to be neat.

6 Problem 5. (20 points) A 1-dimensional sinusoidal traveling wave is propagating in the +x-direction. The wave function is plotted as a function of position when t = 0 and when t = 1 second below: y(x) t=0 t=1 second x (meters) (a) What is the wavelength λ? (b) From the given data, you cannot actually determine the velocity, but you can make some good guesses. What is the lowest (in magnitude) value of the wave velocity v that is consistent with the graphs above? (c) Assuming the velocity you just calculated, calculate the frequency f. (d) Calculate the value of the wave function y(x, t) at x = 9 meters when t = 3 seconds and when t = 3.1 seconds. Don t forget to be neat. Neatness helps!

7 Problem 6. (20 points) A car is travelling at a constant speed of 30 meters/sec. In the car is a loudspeaker making a loud 100 Hz tone. A person is standing stationary on the ground, also with a loudspeaker making a constant 100 Hz tone. 30 m/s The car driver hears two tones: his loudspeaker and the Doppler-shifted tone from the pedestrian. The pedestrian also hears two tones: his own loudspeaker and the Doppler-shifted tone from the car. Calculate the beat-note (that is, the difference between the two tones) heard by each person, and indicate which is which. Take the speed of sound to be 300 meters/second for this problem. Present your work neatly and clearly.