Chapter 16
Wave Motion. Solutions of Selected
Problems
16.1
Problem 16.18 (In the text book)
A transverse sinusoidal wave on a string has a period T = 25.0 ms and travels in the
negative x direction with a speed of 30.0 m/s. At t = 0, a particle on the string at x = 0
has a transverse position of 2.00 cm and is traveling downward with a speed of 2.00 m/s.
(a) What is the amplitude of the wave?
(b) What is the initial phase angle?
(c) What is the maximum transverse speed of the string?
(d) Write the wave function for the wave
.
Solution
2
16.2
CHAPTER 16. WAVE MOTION. SOLUTIONS OF SELECTED PROBLEMS
Problem 16.32 (In the text book)
A light string of mass m and length L has its ends tied to two walls that are separated by
the distance D. Two objects, each of mass M , are suspended from the string as in Figure
(16.32). If a wave pulse is sent from point A, how long does it take to travel to point B?
Figure 16.32:
Solution
Physics XXX:Course Name, Chapter 16
Semester
Ahmed H. Hussein
16.3. PROBLEM 16.44 (IN THE TEXT BOOK)
16.3
3
Problem 16.44 (In the text book)
Show that the wave function y = eb(xvt) is a solution of the linear wave equation (Eq. 16.27),
where b is a constant.
Solution
Physics XXX:Course Name, Chapter 16
Semester
Ahmed H. Hussein
4
16.4
CHAPTER 16. WAVE MOTION. SOLUTIONS OF SELECTED PROBLEMS
Problem 16.54 (In the text book)
A block of mass M hangs from a rubber cord. The block is supported so that the cord is
not stretched. The unstretched length of the cord is L◦ and its mass is m, much less than
M . The “spring constant” for the cord is k. The block is released and stops at the lowest
point.
(a) Determine the tension in the string when the block is at this lowest point.
(b) What is the length of the cord in this “stretched” position?
(c) Find the speed of a transverse wave in the cord if the block is held in this lowest position.
Solution
Physics XXX:Course Name, Chapter 16
Semester
Ahmed H. Hussein
16.5. PROBLEM 16.69 (IN THE TEXT BOOK)
16.5
5
Problem 16.69 (In the text book)
A string on a musical instrument is held under tension T and extends from the point x = 0
to the point x = L. The string is overwound with wire in such a way that its mass per unit
length µ(x) increases uniformly from µ◦ at x= 0 to µL at x = L.
(a) Find an expression for µ(x) as a function of x over the range 0 ≤ x ≤ L.
(b) Show that the time interval required for a transverse pulse to travel the length of the
string is given by
√
2L µL + µ◦ + µL µ◦
√ √
∆t =
√ 3 T
µL + µ◦
Solution
Physics XXX:Course Name, Chapter 16
Semester
Ahmed H. Hussein