In Module 7 you described oscillatory motion in terms of period and frequency. In your examination of simple harmonic motion, you learned that it is the motion of an object due to a restoring force that is directly proportional to and opposite of its displacement from an equilibrium position. You studied the relationships among displacement, acceleration, velocity, and time for the simple harmonic motion in a frictionless, horizontal mass-spring system; and you looked at these relationships in reference to pendulums. You were able to determine the relationships among kinetic, gravitational potential, and total mechanical energies of a mass executing simple harmonic motion. You were also able to calculate these energies. Finally, you examined mechanical resonance and its impact in the everyday world.
Throughout this module, you discovered many examples of oscillatory motion in the world around you. You began by looking at oscillatory motion present in insects, guitars, pianos, and weighted springs. You expanded your studies to include pendulums, clocks, and metronomes. Perhaps the most dramatic examples of oscillatory motion that you examined related to mechanical resonance. A positive application of mechanical resonance is the quartz watch. A negative, and potentially deadly, application was evident when you looked at the Tacoma Narrows Bridge incident.
In Module 8 you began by looking at mechanical waves as particles of a medium that are moving in simple harmonic motion. From there, you were able to compare and contrast energy transmission by matter that moves and by waves. You looked at the direction of the motion of the particles and how it compared to the direction of the propagation of the wave. You learned that this factor determined whether the wave was a longitudinal wave or a transverse wave. As you examined longitudinal and transverse waves, you learned the terminology that allowed you to better define and describe them. You looked at the relationship between the speed of a wave and the characteristics of the medium. You applied the universal wave equation to help solve problems, and you examined the effects of each variable in the equation. You looked at the reflections of waves, the conditions for constructive and destructive interference of waves, and the conditions for acoustic resonance. Finally, you analyzed the phenomenon called the Doppler effect.
Your studies in this module showed that when a wave is displaced from its equilibrium position, it stores elastic potential energy. That energy is transmitted through the medium by the sequential displacement of the medium as the wave pulse moves through it. Energy is thereby transferred through the medium without the transmission of matter. You have seen how the application of acoustic phenomena in medicine, industry, and technology has provided many positive solutions to practical problems. You have learned about the destructive forces of waves and their implications for structural design.