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35. Interference
Assignment is due at 2:00am on Wednesday, January 17, 2007
Credit for problems submitted late will decrease to 0% after the deadline has passed.
The wrong answer penalty is 2% per part. Multiple choice questions are penalized as described in the online help.
The unopened hint bonus is 2% per part.
You are allowed 4 attempts per answer.
A really simple introductory look at interference
A Simple Introduction to Interference
Learning Goal:
To understand the basic principles underlying interference.
One of the most important properties of waves is the
principle of superposition
. The principle of superposition for
waves states that when two waves occupy the same point, their effect on the medium adds algebraically. So, if two
waves would individually have the effect "+1" on a specific point in the medium, then when they are both at that
point the effect on the medium is "+2." If a third wave with effect "2" happens also to be at that point, then the
total effect on the medium is zero. This idea of waves adding their effects, or canceling each other's effects, is the
source of
interference
.
First, consider two wave pulses on a string, approaching each other. Assume that each moves with speed
meter
per second. The figure shows the string at time
. The effect of each wave
pulse on the string (which is the medium for these wave pulses) is to displace
it up or down. The pulses have the same shape, except for their orientation.
Assume that each pulse displaces the string a maximum of
meters, and that
the scale on the
x
axis is in meters.
Part A
At time
, what will be the displacement
at point
?
Express your answer in meters, to two significant figures.
ANSWER:
=
0
Part B
Choose the picture that most closely represents what the rope will actually look like at time
.
ANSWER:
A
B
C
D
The same process of superposition is at work when we talk about continuous waves instead of wave pulses.
Consider a sinusoidal wave as in the figure.
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Part C
How far
to the left would the original sinusoidal wave have to be shifted to give a wave that would completely
cancel the original? The variable
in the picture denotes the wavelength of the wave.
Express your answer in terms of
.
ANSWER:
=
Part D
In talking about interference, particularly with light, you will most likely speak in terms of phase differences, as
well as wavelength differences. In the mathematical description of a sine wave, the phase corresponds to the
argument of the sine function. For example, in the function
, the value of
at a particular point is the
phase of the wave at that point. Recall that in radians a full cycle (or a full circle) corresponds to
radians. How
many radians would the shift of half a wavelength from the previous part correspond to?
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