Chapter 15: Wave Motion 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.

Course Overview http://chem.winthrop.edu/courses Webpage Syllabus Class notes The Class time is 75 minutes MWF No Cell phones, tablets or Computers are allowed in class Office: SIMS, 203 Office Hours: T 10:00-11:00, W 1:00 - 3:00, or by appointment

Webpage and Class notes http://chem.winthrop.edu/

Syllabus- Attendance Although roll is not formally taken in class, I strongly recommend regular attendance. The course has a significant component of interactive learning, and the activities done in class reinforce the material discussed. If there is a reason that you must miss class, please talk with me to make arrangements to cover the material. The attendance policy described in the Winthrop University undergraduate catalog will be followed.

Homework 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. if I notice that the homework is copied from the solutions manual, I will not grade it, and the 5% homework grade will be added to the exams grade.

Quizzes-Recitation Lecture: The PHY 212 lecture is a flipped model class, you are required to read the chapter’s parts in the schedule posted online before coming to class, I will show some videos or have a demo, explain the concepts and solve problems. There will be a 20 minutes quiz every Friday at the beginning of lecture. The equations are not provided for the quizzes. There will be a recitation on Fridays, where I go through problems solving.

Exams There will be three in class exams and a final. The three exams are 75 minutes duration. Notes and your book are not allowed during the exam. All relevant equations and physical constants will be provided. The final exam will be two hours and 30 minutes and will cover early portions of the course so you must review the entire course material.

Three in Class exams 10% each Quizzes 10% Final Exam 30 % Lab 25% If you are going to miss a test, you must notify me in advance (preferably one week) so alternate arrangements can be made. If you miss a test and your absence is not excused, a grade of zero points must be assessed for that particular piece of work. You must take the 75 minutes exams as well as the final exam in order to pass the course. Grading: Homework 5% Three in Class exams 10% each Quizzes 10% Final Exam 30 % Lab 25%

Labs MLK day (Monday 21th ) lab session will be today Labs start on Monday, January 14, 2018 Do not miss any laboratory. You will receive "0" for all missed laboratories. Lab exam is on the last day of classes. Lab exam is 25% of the total lab grade

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 15-2. Motion of a wave pulse to the right. Arrows indicate velocity of cord particles.

15-1 Characteristics of Wave Motion Wave characteristics: Amplitude, A Wavelength, λ Frequency, f and period, T Wave velocity, Figure 15-3. Characteristics of a single-frequency continuous wave moving through space. T

15-2 Types of Waves: Transverse and Longitudinal Figure 15-4. (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).

Transverse and longitudinal waves https://www.youtube.com/watch?v=TfYCnOvNnFU

Sound It Out Does a longitudinal wave, such as a sound wave, have an amplitude? 1) yes 2) no 3) it depends on the medium the wave is in  low high normal air pressure x A Click to add notes

Sound It Out 1) yes 2) no 3) it depends on the medium the wave is in Does a longitudinal wave, such as a sound wave, have an amplitude?  All wave types—transverse, longitudinal, surface—have all of these properties: wavelength, frequency, amplitude, velocity, period. low high normal air pressure x A

The Wave 2) longitudinal wave 3) lateral wave 4) transverse wave At a football game, the “wave” might circulate through the stands and move around the stadium. In this wave motion, people stand up and sit down as the wave passes. What type of wave would this be characterized as? 1) polarized wave 2) longitudinal wave 3) lateral wave 4) transverse wave 5) soliton wave Click to add notes

The Wave 2) longitudinal wave 3) lateral wave 4) transverse wave At a football game, the “wave” might circulate through the stands and move around the stadium. In this wave motion, people stand up and sit down as the wave passes. What type of wave would this be characterized as? 1) polarized wave 2) longitudinal wave 3) lateral wave 4) transverse wave 5) soliton wave The people are moving up and down, and the wave is traveling around the stadium. Thus, the motion of the wave is perpendicular to the oscillation direction of the people, and so this is a transverse wave.

Transverse waves Disturbance is perpendicular to the direction of the wave propagation Examples: Strings Electromagnetic http://www.ncat.edu/~gpii/

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. Disturbance is parallel to the direction of the wave propagation Figure 15-5. Production of a sound wave, which is longitudinal, shown at two moments in time about a half period (1/2 T) apart.

15-2 Types of Waves: Transverse and Longitudinal The velocity of a transverse wave only on a cord is given by:   As expected, the velocity increases when the tension increases, and decreases when the mass increases. Figure 15-7. 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.)

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. The cupper density is=8.9X 103kg/m3 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.

15-2 Types of Waves: Transverse and Longitudinal Problem 6. (II): A cord of mass 0.65 kg is stretched between two supports 8.0 m apart. If the tension in the cord is 140 N, how long will it take a pulse to travel from one support to the other?

15-4 Mathematical Representation of a Traveling Wave Suppose the shape of a wave is given by: D(x) is the displacement of the wave Figure 15-13. In time t, the wave moves a distance vt.

15-4 Mathematical Representation of a Traveling Wave After a time t, the wave crest has traveled a distance vt, so we write: Or:   with , k is the wave number

15-4 Mathematical Representation of a Traveling Wave Example 15-5: A traveling wave. The left-hand end of a long horizontal stretched cord oscillates transversely in SHM with frequency f = 250 Hz and amplitude 2.6 cm. The cord is under a tension of 140 N and has a linear density μ = 0.12 kg/m. At t = 0, the end of the cord has an upward displacement of 1.6 cm and is falling. Determine (a) the wavelength of waves produced and (b) the equation for the traveling wave. Figure 15-14. Example 15-5. The wave at t = 0 (the hand is falling). Not to scale. Solution: a. The wave velocity is 34 m/s, so the wavelength is 14 cm. b. From the amplitude and the displacement at t = 0, we find that the phase angle is 0.66 rad. Then D = 0.026 sin(45x – 1570t + 0.66).

Problem 24