MasteringPhysics: Assignment Print View
http://session.masteringphysics.com/myct/assignmentPrint?assignm...
1 of 18
11/26/07 10:17 PM
[
Print View
]
physics 2211
MP17: Chapter 21
Due at 5:30pm on Monday, December 10, 2007
View Grading
Details
Creating a Standing Wave
Learning Goal:
To see how two traveling waves of the same frequency create a standing wave.
Consider a traveling wave described by the formula
.
This function might represent the lateral displacement of a string, a local electric field, the position of the surface of a
body of water, or any of a number of other physical manifestations of waves.
Part A
Which one of the following statements about the wave described in the problem introduction is correct?
ANSWER:
The wave is traveling in the
direction.
The wave is traveling in the
direction.
The wave is oscillating but not traveling.
The wave is traveling but not oscillating.
Part B
Which of the expressions given is a mathematical expression for a wave of the same amplitude that is traveling in
the opposite direction? At time
this new wave should have the same displacement as
, the wave
described in the problem introduction.
ANSWER:
The principle of
superposition
states that if two functions each separately satisfy the wave equation, then the sum (or
difference) also satisfies the wave equation. This principle follows from the fact that every term in the wave equation
is linear in the amplitude of the wave.
[
Print
]
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
MasteringPhysics: Assignment Print View
http://session.masteringphysics.com/myct/assignmentPrint?assignm...
2 of 18
11/26/07 10:17 PM
Consider the sum of two waves
, where
is the wave described in Part A and
is the
wave described in Part B. These waves have been chosen so that their sum can be written as follows:
.
This form is significant because
, called the envelope, depends only on position, and
depends only on
time. Traditionally, the time function is taken to be a trigonometric function with unit amplitude; that is, the overall
amplitude of the wave is written as part of
.
Part C
Find
and
. Keep in mind that
should be a trigonometric function of unit amplitude.
Hint C.1 A useful identity
A useful trigonometric identity for this problem is
.
Hint C.2 Applying the identity
Since you really need an identity for
, simply replace
by
in the identity from Hint C.1, keeping
in mind that
.
Express your answers in terms of
,
,
,
, and
. Separate the two functions with a
comma.
ANSWER:
,
=
Part D
Which one of the following statements about the superposition wave
is correct?
ANSWER:
This wave is traveling in the
direction.
This wave is traveling in the
direction.
This wave is oscillating but not traveling.
This wave is traveling but not oscillating.
A wave that oscillates in place is called a
standing wave
. Because each part of the string oscillates with the same
phase, the wave does not appear to move left or right; rather, it oscillates up and down only.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 DUNCAN
 Physics, Assignment Print View

Click to edit the document details