General Physics III Practice Exam II Fall 2007

General Physics III Practice Exam II Fall 2007
1. A string fixed at both ends is vibrating in a standing wave at its fundamental resonance frequency. The
string vibrates according to the equation
y(x,t) = 0.02 sin(πx/2)cos(20πt)
where x and y are in meters and t is in seconds.
(a) What is the wave speed for the string?
(b) What is the length of the string?
(c) If the string has a mass of 50g, what is the tension in the string?
(d)
(e)
What is the maximum speed of a segment of the string?
The vibrating string described above is placed over the open end of a tube filled with air, The opposite end
of the tube is closed. The vibrating string generates a standing wave in the air column inside the tube at its
fundamental frequency. What is the length of the tube? (The speed of sound in air is 340 m/s.)

2A
A bat flies towards a wall at a speed of 5.0 m/s. As it flies, the bat emits an ultrasonic sound wave with
frequency 30,000 Hz. What frequency does the bat hear in the reflected wave?
2B. You have three tuning forks, A, B and C. Fork B has a frequency of 440 Hz. When A and B are sounded
together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4Hz.
(a) What are the possible frequencies of A and C?
(b) What beat frequencies are possible when A and C are sounded together?

3.A. Two students are performing an experiment. Two springs are connected at a point J that is
equidistant from the students' hands, as shown in the top-view diagram below. Student 2 creates a pulse
having a displacement on only one side of the spring. A short time later, students 1 and 2 receive pulses
on opposite sides of the spring.
i. Is the tension in spring A greater than, less than or equal to the tension in spring B?
Explain your reasoning.
ii.
For this experiment, is the reflection at point J like that at a fixed end or a free end?
If there is not enough information to tell, state so explicitly. Explain.
iii.
Who received a pulse first, student 1 or student 2? If there is not enough information to tell, state
so explicitly. Explain your reasoning.
3.B.
The rectangular metal tank shown in the diagram is filled with an unknown liquid. The observer, whose
eye is level with the top of the tank, can just see corner E. Calculate the index of refraction of this liquid.
.

4A. Two converging lenses (lens 1 and lens 2) with focal length f 1 = 20.0 cm and f 2 = 25.0 cm are placed
20.0 cm apart along their common optical axis. An object is placed 60.0 cm in front of lens 1.
Determine:
(a) the position of the image from lens 1, if it is real or virtual, upright or inverted and its magnification;
(b) the position of the final image from lens 2, if it is real or virtual, upright or inverted and its magnification.
(c) Sketch a diagram showing the two lenses, the object (as an upright arrow), the image from lens 1
and the final image.
4B. Violet light of wavelength 415 nm passes through a single narrow slit and creates a central diffraction peak
which has a width (distance between the first minima on both sides of the central maximum) of 9.20 cm on
a screen that is 2.55 m from the slit. How wide is the slit?
4C. How many lines per centimeter must diffraction grating have such that there will be no 2 nd order maximum
for light of any wavelength in the visible region (400 nm to 700 nm)?