Exploring Mechanical Waves: Properties and Dynamics

1. Chapter 15 Mechanical Waves

2. 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

3. 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.

4. 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.

5. Periodic waves • A detailed look at periodic transverse waves will allow us to extract parameters.

6. 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.

7. 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).

8. 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 15.1. • Consider Example 15.2.

9. 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.

10. The speed of a transverse wave • In the first method we will consider a pulse on a string. • Figure 15.11 will show one approach.

11. The speed of a transverse wave II • We can take a second glance at the speed of a transverse wave on a string. Figure 15.13 will set the stage. • Follow Example 15.3 and refer to Figure 15.14.

12. 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/r2. • Follow Example 15.5 to see the inverse-square law in action.

13. Wave interference, boundaries, and superposition • Waves in motion from one boundary (the source) to another boundary (the endpoint) will travel and reflect.

14. 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.

15. 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.

16. 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.

17. 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 15.29 provides many such multidimensional shapes. • Regard Figure 15.29 and then follow Examples 15.7 and 15.8.