21 Mp Hw
Chapter 21 Homework
Due: 11:59pm on Sunday, July 28, 2013
You will receive no credit for items you complete after the assignment is due. Grading Policy
Problem 21.1
The figure is a snapshot graph at = 0 of two waves approaching each other at 1.0 stacked vertically, showing the string at 1 intervals from = 1 to = 6 . . Draw six snapshot graphs,
Part A
=1 ANSWER:
Answer Requested
Part B
=2 ANSWER:
Answer Requested
Part C
=3 ANSWER:
Answer Requested
Part D
=4 ANSWER:
Answer Requested
Part E
=5 ANSWER:
Answer Requested
Part F
=6 ANSWER:
Answer Requested
Normal Modes and Resonance Frequencies
Learning Goal: To understand the concept of normal modes of oscillation and to derive some properties of normal modes of waves on a string. A normal mode of a closed system is an oscillation of the system in which all parts oscillate at a single frequency. In general there are an infinite number of such modes, each one with a distinctive frequency and associated pattern of oscillation. Consider an example of a system with normal modes: a string of length held fixed at both ends, located at and . Assume that waves on this string propagate with speed . The string extends in the x direction, and the waves are transverse with displacement along the y direction. In this problem, you will investigate the shape of the normal modes and then their frequency. The normal modes of this system are products of trigonometric functions. (For linear systems, the time dependance of a normal mode is always sinusoidal, but the spatial dependence need not be.) Specifically, for this system a normal mode is described by
Part A
The string described in the problem introduction is oscillating in one of its normal modes. Which of the following statements about the wave in the string is correct?
Hint 1. Normal mode constraints
The key constraint with normal modes is that there are two spatial boundary conditions, , which correspond to the
Due: 11:59pm on Sunday, July 28, 2013
You will receive no credit for items you complete after the assignment is due. Grading Policy
Problem 21.1
The figure is a snapshot graph at = 0 of two waves approaching each other at 1.0 stacked vertically, showing the string at 1 intervals from = 1 to = 6 . . Draw six snapshot graphs,
Part A
=1 ANSWER:
Answer Requested
Part B
=2 ANSWER:
Answer Requested
Part C
=3 ANSWER:
Answer Requested
Part D
=4 ANSWER:
Answer Requested
Part E
=5 ANSWER:
Answer Requested
Part F
=6 ANSWER:
Answer Requested
Normal Modes and Resonance Frequencies
Learning Goal: To understand the concept of normal modes of oscillation and to derive some properties of normal modes of waves on a string. A normal mode of a closed system is an oscillation of the system in which all parts oscillate at a single frequency. In general there are an infinite number of such modes, each one with a distinctive frequency and associated pattern of oscillation. Consider an example of a system with normal modes: a string of length held fixed at both ends, located at and . Assume that waves on this string propagate with speed . The string extends in the x direction, and the waves are transverse with displacement along the y direction. In this problem, you will investigate the shape of the normal modes and then their frequency. The normal modes of this system are products of trigonometric functions. (For linear systems, the time dependance of a normal mode is always sinusoidal, but the spatial dependence need not be.) Specifically, for this system a normal mode is described by
Part A
The string described in the problem introduction is oscillating in one of its normal modes. Which of the following statements about the wave in the string is correct?
Hint 1. Normal mode constraints
The key constraint with normal modes is that there are two spatial boundary conditions, , which correspond to the