Physics 208 ST Quiz 1

Lecturer: Dr. Min Xu

Feb 26, 2002
LAST NAME: ___________________________________________________________________________________________________ FIRST NAME: __________________________________________________________________________________________________ SS# (last 4 digits): _____________________________________________________________________________________________

General Instruction

You have 1 hour 30 minutes to answer 5 questions on this exam. Work each problem only on the sheet provided for this problem, using the back if necessary. Please write the name and recitation section 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. (20 points) A certain transverse wave is described by

t x y(x,t) = (6.50mm)sin2p( --------+ -------) 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.

2. (20 points) The Doppler effect can be used to estimate the speed of a moving sound source. A police siren emits a sinusoidal wave with frequency fs = 300Hz. The speed of sound is 340m/s. A musician is standing by the road and hears the siren changes its pitch when the siren moves toward and then away from him.


(a) (5 points) Does the pitch of the siren become higher or lower when the siren moves toward and then away from the musician?
(b) (15 points) Find the speed of the siren if the musician hears a 20Hz change in pitch.

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.

5. (20 points) Wave interference can be found in many examples. Take any two of the following three questions and explain using the concept of interference.


(a) (10 points) A standing wave can propagate in an ends-fixed string if the length of the string L = (n + 1/2)c where n is integer and c is the wave length.
(b) (10 points) Tune a string of a piano by relying on beats..
(c) (10 points) The contact point of an air wedge formed by two glass plates looks dark.