Chapter 15: Wave Motion

Syllabus15-1 Characteristics of Wave Motion15-2 Types of Waves: Transverse and Longitudinal15-3 Energy Transported by Waves15-4 Mathematical Representation of a Traveling Wave15-5 The Wave Equation15-6 The Principle of Superposition15-7 Reflection and Transmission

HW1: Pb.7, Pb.11,Pb.23, Pb.30,Pb.37, and Pb.42, due Wednesday 21

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%

• 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.

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.

15-1 Characteristics of Wave Motion

Wave characteristics:

• Amplitude, A

• Wavelength, λ

• Frequency, f and period, T

• Wave velocity,

15-1 Characteristics of Wave Motion

T

Harmonic Waves

T

1

f v f

T

v = wave speed for a traveling wave-speed a pulse moves

Periodic waves with a sinusoidal shape

2f

vm

A

am

A2

Speed that the medium vibrates

Angular frequency

The motion of particles in a wave can be either perpendicular to the wave direction (transverse) or parallel to it (longitudinal).

15-2 Types of Waves: Transverse and Longitudinal

Transverse

Longitudinal

Transverse waves

• Disturbance is perpendicular to the direction of the wave propagation

Examples:

StringsElectromagnetic

http://www.ncat.edu/~gpii/

Longitudinal waves

• Disturbance is parallel to the direction of the wave propagation

Examples:Sound

Fluid waves (except on surface)

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

Sound waves are longitudinal waves: Drum Membrane

15-2 Types of Waves: Transverse and Longitudinal

A vibrating Drum is compressing and rarifying the air that in contact with it producing a longitudinal wave

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.

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 0.750 seconds after it landed. Determine the tension in the wire.

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.

or

E: Elastic Modulusof the material

B: Bulk Modulusof the material

E and B are in N/m2

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:

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.

15-3 Energy Transported by Waves

S is a cross sectional area through which a wave travel