Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley PowerPoint ® Lectures for University Physics, Twelfth Edition – Hugh D. Young and Roger A. Freedman Lectures by James Pazun Chapter 15 Mechanical Waves

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Goals for Chapter 15 To study waves and their properties To consider wave functions and wave dynamics To calculate the power in a wave To consider wave superposition To study standing waves on a string

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Introduction At right, you’ll see the piles of rubble from a highway that absorbed just a little of the energy from a wave propagating through the earth in California. In this chapter, we’ll focus on ripples of disturbance moving through various media.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Types of mechanical waves Waves that have compressions and rarefactions parallel to the direction of wave propagation are longitudinal. Waves that have compressions and rarefactions perpendicular to the direction of propagation.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Periodic waves A detailed look at periodic transverse waves will allow us to extract parameters.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Periodic waves II A detailed look at periodic longitudinal waves will allow us to extract parameters just as we did with transverse waves. Refer to Example 15.1.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Mathematical description of a wave When the description of the wave needs to be more complete, we can generate a wave function with y(x,t).

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Graphing wave functions Informative graphic presentation of a wave function is often either y-displacement versus x-position or y-displacement versus x-time. Refer to Problem-Solving Strategy Consider Example 15.2.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Particle velocity and acceleration in a sinusoidal wave From the wave function, we have an expression for the kinematics of a particle at any point on the wave.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley The speed of a transverse wave In the first method we will consider a pulse on a string. Figure will show one approach.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley The speed of a transverse wave II We can take a second glance at the speed of a transverse wave on a string. Figure will set the stage. Follow Example 15.3 and refer to Figure

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Wave intensity Go beyond the wave on a string and visualize, say … a sound wave spreading from a speaker. That wave has intensity dropping as 1/r 2. Follow Example 15.5 to see the inverse-square law in action.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Wave interference, boundaries, and superposition Waves in motion from one boundary (the source) to another boundary (the endpoint) will travel and reflect.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Vertical applications of SHM As wave pulses travel, reflect, travel back, and repeat the whole cycle again, waves in phase will add and waves out of phase will cancel.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Standing waves on a string Fixed at both ends, the resonator was have waveforms that match. In this case, the standing waveform must have nodes at both ends. Differences arise only from increased energy in the waveform.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley The formation of a standing wave The process seems complicated at first, but it is nothing more than waveforms adding constructively when they’re in phase and destructively when they’re not. Refer to Problem- Solving Strategy 15.2 and Example 15.6.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Complex standing waves As the shape and composition of the resonator change, the standing wave changes also. Regard Figure 15.27, a multidimensional standing wave. Figure provides many such multidimensional shapes. Regard Figure and then follow Examples 15.7 and 15.8.