Physics 208 GH Quiz 1

Lecturer: Dr. Min Xu

Sept 25, 2002
LAST NAME: ___________________________________________________________________________________________________ FIRST NAME: __________________________________________________________________________________________________ SS# (last 4 digits): _____________________________________________________________________________________________

General Instruction

You have 1 hour 30 minutes to answer 4 questions on this exam. Work each problem only on the sheet provided for this problem, using the back if necessary. Please write the name on each sheet at the top of the page.

You must indicate the reasoning and show all the steps.

If you are unable to obtain the answer to part of a problem and you need the answer to solve the subsequent parts, use an appropriate symbol for the answer to the previous part and solve in terms of that symbol.

1. (40 points) A certain transverse wave is described by

y(x,t) = (6.50mm) sin 2p(---t----+ --x----) 0.0360s 28.0cm
(1)


(a) (10 points) Determine the wave’s amplitude, wavelength, frequency, speed of propagation, and direction of propagation.
(b) (10 points) Draw a figure at time t = 0 of the wave. Explain the moving direction of the particle at x = 0 at t = 0 and label that in the figure.
(c) (10 points) Suppose the wave is propagating on a string with a linear mass density 0.05kg/m, find the tension of the string and the power required to generate the wave.
(d) (10 points) Now assume the wave y(x,t) is reflected at the fixed end of the string at x = 0, a standing wave is then formed from the interference of this incident wave y(x,t) and the reflected wave yref(x,t). Find yref(x,t) and the standing wave y(x,t) + yref(x,t).

2. (20 points) The Doppler effect can be used to estimate the speed of a moving sound source. A police car moves with speed v and emits a sinusoidal wave with frequency fs = 300Hz. The speed of sound is 340m/s.


(a) (5 points) A musician is standing by the road. What is the perceived frequency f1 by the musician of the sound wave when the car is moving toward the musician?
(b) (5 points) What is the perceived frequency f2 when the car is moving away from the musician?
(c) (10 points) Find the speed v of the car if the change of the frequencies Df = |f1 - f2| = 20Hz.

3. (20 points) Image Formation. A kid is standing before a convex mirror whose radius is 4m. The kid is 2m before the mirror and he is 1m tall.


(a) (10 points) Use a graphical method to obtain the image of the kid and the height of that image by measuring using a ruler.
(b) (10 points) Confirm the previous result using the object-image relation
1 1 1 -+ --= --. s s' f
(2)

Explain the signs of s,s' and f in your calculation.

4. (20 points) We have discussed that the apparent depth of a swimming pool is about 3/4 of the real depth viewed by a person standing by the pool. Assume a fish inside the swimming pool is under the feet of the person standing by the pool, and the person is 1.8m tall.


(a) (10 points) Is the apparent height of the person in the eyes of the fish larger or smaller than the real height? Draw a figure to support your reasoning.
(b) (10 points) Find the apparent height of the person.