12/21/2016
HW#1
HW#1 Due: 11:59am on Tuesday, December 6, 2016 You will receive no credit for items you complete after the assignment is due. Grading Policy
Problem 20.1 The wave speed on a string is 145 m/s when the tension is 75.0 N .
Part A What tension will give a speed of 180 m/s ? Express your answer with the appropriate units. ANSWER: 116 N
Correct
Standard Expression for a Traveling Wave Learning Goal: To understand the standard formula for a sinusoidal traveling wave. One formula for a wave with a y displacement (e.g., of a string) traveling in the x direction is .
y(x, t) = A sin(kx − ωt)
All the questions in this problem refer to this formula and to the wave it describes.
Part A Which of the following are independent variables?
Hint 1. What are independent variables? Independent variables are those that are freely varied to control the value of the function. The independent variables typically appear on the horizontal axis of a plot of the function. ANSWER:
https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=4709300
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x
t
only
only
A
only
only
k
only x and t ω
ω
and t
A
and k and ω
Correct
Part B Which of the following are parameters that determine the characteristics of the wave?
Hint 1. What are parameters? Parameters are constants that determine the characteristics of a particular function. For a wave these include the amplitude, frequency, wavelength, and period of the wave. ANSWER:
x
t
only
only
A
only
only
k
only x and t ω
ω
and t
A
and k and ω
Correct
Part C What is the phase ϕ(x, t) of the wave? Express the phase in terms of one or more given variables ( A, k, x, t, and ω) and any needed constants like π. https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=4709300
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Hint 1. Definition of phase The phase is the argument of the trig function, which is expressed in radians. ANSWER: =
ϕ(x, t)
kx − ωt
Correct
Part D What is the wavelength λ of the wave? Express the wavelength in terms of one or more given variables ( A, k, x, t, and ω) and any needed constants like π.
Hint 1. Finding the wavelength Consider the form of the wave at time t = 0 . The wave crosses the y axis, sloping upward at x = 0. The wavelength is the x position at which the wave next crosses the y axis, sloping upward (i.e., the length of one complete cycle of oscillation). ANSWER: =
λ
2π k
Correct
Part E What is the period T of this wave? Express the period in terms of one or more given variables ( A, k, x, t, and ω) and any needed constants like π. ANSWER: T
=
f
Incorrect; Try Again; 2 attempts remaining
Part F What is the speed of propagation v of this wave? Express the speed of propagation in terms of one or more given variables ( A, k, x, t, and ω) and any needed constants like π. https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=4709300
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Hint 1. How to find v If you've done the previous parts of this problem, you have found the wavelength and the period of this wave. The speed of propagation is a function of these two quantities: v = λ/T .
ANSWER: v
=
ω k
Correct
Conceptual Question 20.4 The figure shows a snapshot graph and a history graph for a wave pulse on a stretched string. They describe the same wave from two perspectives.
Part A In which direction is the wave traveling? ANSWER: to the right to the left
Correct
Part B What is the speed of this wave? Express your answer with the appropriate units. ANSWER: https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=4709300
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HW#1
= 200
cm s
Correct
Problem 20.03
Part A The vertical displacement y(x,t) of a string stretched along the horizontal xaxis is given by y(x,t) = (6.00 mm) cos[(3.25 m 1)x (7.22 rad/s)t]. (a) What is the minimum time for each complete cycle of the wave? ANSWER: s
Part B (b) What is the distance between adjacent crests of the wave? ANSWER: 20.42
m
Incorrect; Try Again; 5 attempts remaining
Part C (c) How fast does this wave travel? ANSWER: m/s
Score Summary: Your score on this assignment is 68.2%. You received 2.73 out of a possible total of 4 points.
https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=4709300
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