1. A string is under tension F. A theoretical profile function for a pulse on the string is given below. The function is piecewise defined in regions I (x < -a), and III (x > a) as positive and negative inverse square functions and in region II (-a≤ x ≤ a) as a cubic function. 80(x) = -2 3 A (#) -² ¾A ((2)³ — § (4)) -A (%) -² -2 - x-a 3/3 ( ³ ³ ) ) − a ≤ x ≤ a - x > a (a) This function is continuous if at the points any two regions meet, the function in each region eval- uates to the same value. Show this is the case at x = a and x = -a. (b) This function is smooth if at the points any two regions meet, the derivative of the function in each region evaluates to the same value. Show this is the case at x = a and x = -a. (c) Find the total energy, E = K + U, of the pulse assuming it propagates as a traveling wave. This should be in terms of F, a and A.
1. A string is under tension F. A theoretical profile function for a pulse on the string is given below. The function is piecewise defined in regions I (x < -a), and III (x > a) as positive and negative inverse square functions and in region II (-a≤ x ≤ a) as a cubic function. 80(x) = -2 3 A (#) -² ¾A ((2)³ — § (4)) -A (%) -² -2 - x-a 3/3 ( ³ ³ ) ) − a ≤ x ≤ a - x > a (a) This function is continuous if at the points any two regions meet, the function in each region eval- uates to the same value. Show this is the case at x = a and x = -a. (b) This function is smooth if at the points any two regions meet, the derivative of the function in each region evaluates to the same value. Show this is the case at x = a and x = -a. (c) Find the total energy, E = K + U, of the pulse assuming it propagates as a traveling wave. This should be in terms of F, a and A.
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter16: Waves
Section: Chapter Questions
Problem 145CP: A pulse moving along the x axis can be modeled as the wave function y(x,t)=4.00me( x+( 2.00m/s )t...
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Question
a
(a) This function is continuous if at the points any two regions meet, the function in each region evaluates to the same value. Show this is the case at x = a and x = -a.
(b) This function is smooth if at the points any two regions meet, the derivative of the function in each region evaluates to the same value. Show this is the case at x = a and x = —a.
(c) Find the total energy, E = K + U, of the pulse assuming it propagates as a traveling wave. This
should be in terms of F, a and A.
part a b and c I need to show all work
Transcribed Image Text:1. A string is under tension F. A theoretical profile function for a pulse on the string is given below.
The function is piecewise defined in regions I (x < -a), and III (x > a) as positive and negative inverse
square functions and in region II (-a≤ x ≤ a) as a cubic function.
80(x) =
-2
3
A (#) -²
¾A ((2)³ — § (4))
-A (%) -²
-2
-
x-a
3/3 ( ³ ³ ) ) − a ≤ x ≤ a
-
x > a
(a) This function is continuous if at the points any two regions meet, the function in each region eval-
uates to the same value. Show this is the case at x = a and x = -a.
(b) This function is smooth if at the points any two regions meet, the derivative of the function in each
region evaluates to the same value. Show this is the case at x = a and x = -a.
(c) Find the total energy, E = K + U, of the pulse assuming it propagates as a traveling wave. This
should be in terms of F, a and A.
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