1. Chapter 15: Wave Motion
Syllabus
15-1 Characteristics of Wave Motion
15-2 Types of Waves: Transverse and Longitudinal
15-3 Energy Transported by Waves
15-4 Mathematical Representation of a Traveling Wave
15-5 The Wave Equation
15-6 The Principle of Superposition
15-7 Reflection and Transmission
Chapter opener. Caption: Waves—such as these water waves—spread outward from a source. The source in this case is a small spot of water oscillating up and down briefly where a rock was thrown in (left photo). Other kinds of waves include waves on a cord or string, which also are produced by a vibration. Waves move away from their source, but we also study waves that seem to stand still (“standing waves”). Waves reflect, and they can interfere with each other when they pass through any point at the same time.
HW1: Pb.7, Pb.11,Pb.23, Pb.30,Pb.37, and Pb.42,
due Wednesday 21

2. Syllabus
Office Hours: Tuesday 10:00am-11:00am, and Wednesday 1:00pm-3:00pm or by appointment.
Presence in the labs is required, a missed lab is a 0, unless you are able to make it up.
Homework problems are due on the dates indicated on the class calendar. Your work is due on time, with the exception of reasonable documented excuses. Late work will be docked 50% of face value and 100% after solutions have been posted.
Grading:
Homework 10%
Three in Class exams 10% each
Final Exam 30 %
Lab 25%

3. Tutoring: there is a tutor at the Academic Success Center (ASC).
Her name is Zoe Vernon.
In order to request a tutor through the Center, you must attend one 30-minute Tutee Seminar per academic year.
The first Tutee Seminar for the spring semester will be offered on Friday, January 16th at 1 pm and again at 2pm and continue every Friday through March 13.

4. 15-1 Characteristics of Wave Motion
All types of traveling waves transport energy.
Study of a single wave pulse shows that it is begun with a vibration and is transmitted through internal forces in the medium.
Continuous or periodic waves start with vibrations, too. If the source vibrate sinusoidally, then the wave will have a sinusoidal shape.
Figure Motion of a wave pulse to the right. Arrows indicate velocity of cord particles.

5. 15-1 Characteristics of Wave Motion
Wave characteristics:
Amplitude, A
Wavelength, λ
Frequency, f and period, T
Wave velocity,
Figure Characteristics of a single-frequency continuous wave moving through space. T

6. Harmonic Waves Periodic waves with a sinusoidal shape
Speed that the medium vibrates
Angular frequency
v = wave speed for a traveling wave-speed a pulse moves

7. 15-2 Types of Waves: Transverse and Longitudinal
Figure (a) Transverse wave; (b) longitudinal wave.
The motion of particles in a wave can be either perpendicular to the wave direction (transverse) or parallel to it (longitudinal).

8. Transverse waves
Disturbance is perpendicular to the direction of the wave propagation
Examples:
Strings
Electromagnetic

9. Longitudinal waves
Disturbance is parallel to the direction of the wave propagation
Examples:
Sound
Fluid waves
(except on surface)
Compressions are rarefactions
The First Book of Sound: A Basic Guide to the Science of Acoustics by David C. Knight, Franklin Watts, Inc. New York (1960). p. 80

10. 15-2 Types of Waves: Transverse and Longitudinal
Sound waves are longitudinal waves: Drum Membrane
A vibrating Drum is
compressing and
rarifying the air that in
contact with it producing
a longitudinal wave
Figure Production of a sound wave, which is longitudinal, shown at two moments in time about a half period (1/2 T) apart.

11. 15-2 Types of Waves: Transverse and Longitudinal
The velocity of a transverse wave on a cord is given by:
As expected, the velocity increases when the tension increases, and decreases when the mass increases.
Figure Diagram of simple wave pulse on a cord for derivation of Eq. 15–2.The vector shown in (b) as the resultant of FT + Fy has to be directed along the cord because the cord is flexible. (Diagram is not to scale: we assume v’ << v; the upward angle of the cord is exaggerated for visibility.)

12. 15-2 Types of Waves: Transverse and Longitudinal
Example 15-2: Pulse on a wire.
An 80.0m-long, 2.10mm-diameter copper wire is stretched between two poles. A bird lands at the center point of the wire, sending a small wave pulse out in both directions. The pulses reflect at the ends and arrive back at the bird’s location seconds after it landed. Determine the tension in the wire.
Solution: We need to find the mass per unit length of the wire; this comes from the cross-sectional area and the density of copper (8900 kg/m3). Then the tension is 353 N.

13. 15-2 Types of Waves: Transverse and Longitudinal
The velocity of a longitudinal wave depends on the elastic restoring force of the medium and on the mass density.
E: Elastic Modulus
of the material or
B: Bulk Modulus
of the material
E and B are in N/m2

14. 15-3 Energy Transported by Waves
By looking at the energy of a particle of matter in the medium of a wave, we find:
Then, assuming the entire medium has the same density, we find:
Figure Calculating the energy carried by a wave moving with velocity v.
Therefore, the intensity I ( defined as average power) of a wave is proportional to the square of the frequency and to the square of the amplitude.
S is a cross sectional area through which a wave travel