# PHYS273 WAVES

 Instructor: Kara Hoffman, PhD Assistant Professor of Physics Office: 4336 Toll Physics Building Phone: 301-405-7263 Email: kara@umd.edu Office hours: by appointment Teaching Assistant: Babak Monajemi Office: Room 4223 Office hours: 3:30-5:00pm Email: babakm@wam.umd.edu Course Syllabus: 273 syllabus

## ANNOUNCEMENT: Final Exam PHY 1410 Mon, May 14 8:00 am - 10:00 am

You may bring three recipe cards with equations on it. Remember to bring your calculator!

## Exam 1Exam 1 Solution

### Exam from Prof. Williams Fall 06 classSolution

Note: Prof. Hoffman's exams may be somewhat different in style.

## Homework

### Homework #6 due March 15Solution

fourier_tutorial.pdf SqWave.xls AMWave.xls FourierSpectrum.jpg

Gaussian.xls

### Homework #10 due April 19Solution

WaveReflection.xls

## Topics covered in lecture

Jan 25: H&L Ch 1.1-1.3 T&M: Review Chapter 14
Jan 26: H&L Ch 3 - if you need extra help with complex numbers, see Chapter 1 of French (on reserve in the EPSL library)
Jan 30 more on solving SHM with complex exponentials and H&L Ch 1.4
Feb 1 damped hormonic motion - see H&L section 1.6 and T&M Ch14
Feb 2 Oscillating E&M circuits (H&L 1.4 and T&M Ch 29)
Feb 6 Damped RLC circuits, H&L 1.6, T&M 29-5
Feb 8 and Feb 9 Forced oscillations, H&L Section 1.7 T&M section 29-6, see T&M Appendix pages AP 20-23 for math help with exponential solutions of differential equations
Feb 13 Travelling waves, H&L Chapter 2.1-2.3, reference T&M Chapter 15.1-15.2
Feb 15 The wave equation (H&L Chapter 2, Chapter4 and T&M Chapter 15)
Feb 16 general solutions of the wave equation; energy density (Chapter 4.6)
Feb 20 superposition of waves, beats
Feb 22 wave and group velocities, dispersion
Feb 23 finish chapter 4 (wave equation for longitudinal springs, momentum of a wave)
Feb 27-March 6 Fourier analysis (Chapter 13.1-13.4)
March 9-16 Standing Waves (Chapter 6)
March 27 Spherical waves (Chapter 7)
March 29 The Doppler effect (Chapter 8)
March 30 Sonic booms and Cerenkov radiation (H&L 8.5)
April3 the premittivity and permeability of free space (T&M 30-3 and H&L 9.1)
April 5 review of Maxwell's equations and displacement current (T&M 30-1,30-2)
April 6 EM waves and the Poynting vector (T&M 30-3)
April 10 examples using the Poynting vector and the can crusher (H&L 9.4)
April 12 coax and transmission lines, reflections in transmission lines (H&L 9.3 & 9.6)
April 13 dielectrics, speed of a pulse in a cable
April 17, 19, 26 Diffraction and Interference (H&L Chapter 11)
The rest of the semester Geometrical optics (H&L Chapter 12)

### Learning tools:

electromagnetic can crusher An in depth analysis

mach cone Diagram of mach cone and illustrative example.

Sonic boom Here is a photograph and mpeg video of an F/A-18 breaking the sound barrier.

Doppler effect Here is an applet demonstrating the doppler effect.

Vibrations of a drum head Watch animations of a vibrating drum head.

Formation of a standing wave Here is an animation of standing waves forming on a string with both ends clamped.

wave reflection and transmission Here is an animation of waves reflecting and transmitting at boundaries between two strings of different densities.

Fourier series use this applet to plot a waveform formed by a fourier series.

wave dispersion animations of wave dispersion

Forced oscillations and resonance
Here is a java applet that plots the parameters of an RLC circuit. Play with it. See how the sharpness of the resonance peak changes as you increase and decrease the resistance. See how the resonant frequency changes as you change the capcitance and the inductance. Set the frequency to be on resonance, then off resonance, then click on the radio button for i(t), V(t) and see how the appled voltage and the current changes as a function of the frequency.

Here is an applet that illustrates the mechanical alaogue. Try setting the frequency to the resonant frequency, then look at the "elongation diagram". See how the amplitude gets larger with each successive oscillation.
PHYS273 and PHYS273H
Spring 2007