14: Waves
- Understand the definition of different types of waves.
- Understand how to mathematically describe traveling and standing waves.
- Understand how to model the propagation of a pulse on a rope.
- Understand how to model the energy transported by a wave.
- Understand how to model the interference of waves.
- Understand how standing waves form and how to model them
In this chapter we introduce the tools to describe waves. Waves arise in many different physical systems (the ocean, a string, electromagnetism, etc.), and can be described by a common mathematical framework.
Two waves travel down two identical strings (Figure 14.1). The frequency of the first wave is twice that of the second wave. Which wave will be faster?
- The first wave.
- The second wave.
- The speeds will be the same.
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- 14.2: Mathematical Description of a Wave
- In order to describe the motion of a wave through a medium, we can describe the motion of the individual particles of the medium as the wave passes through. Specifically, we describe the position of each particle using its displacement, D , from its equilibrium position.