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Unformatted text preview: 1 Lesson 5.2 Wave Motion Lesson Objectives: At the end of this lesson students will be able to (i) describe the characteristics wave motion and derive a mathematical expression describing the transverse vibrations of a stretched string. (ii) apply the characteristics of wave motion to solve problems. 1. What is a wave? Fig. 1 on the right shows a stretched string with one end fastened to a support and the other end free to move. If you move the free end of the string briskly up and down, a pulse is generated by the up and down motion of the segments of the string. Each segment executes simple harmonic motion with a definite period and frequency. As each segment is connected to the next by elastic forces, the vibration gets passed on from segment to segment and the pulse you generated moves along the length of the string towards the fixed end. When the pulse reaches the fixed end, it gets reflected. And now we have a pulse moving in the opposite direction. Advancing pulse reflected pulse Fig. 1 The propagation of the pulse along the string is an example of how energy can be made to move along the length of the string without the particles of the string moving away from their respective positions. Each segment executes simple harmonic motion about its own equilibrium position and the vibration gets handed over from segment to segment until it reaches the other end. Using this concept we can define wave motion as kind of energy transfer in a medium due to the vibration of the particles of the medium without the particles themselves moving away from their positions . 2 2. Phase and phase difference: Equilibrium position Upper extreme Lower extreme 1 2 3 4 5 6 7 8 Fig. 2 phase difference in vibration Fig. 2 above shows 8 particles vibrating in simple harmonic motion. Particles 1 and 2 are in the equilibrium position and they are both moving up. These two particles are in the same phase of vibration. Particles 3 and 4 also are in the equilibrium position, but 3 is moving up and 4 is moving down. Particle 4 has completed half of a vibration while particle 1 is just beginning. We can say that particle 4 is half a vibration ahead of particle 1. We can also say that particle 4 is half a period ahead of particle 1. These are two ways to express the phase difference between two vibrating particles. The standard method of expressing phase difference is using the phase angle. When a particle in shm completes one vibration, it describes an angle of 2 π radians. When a particle completes half a vibration, it describes an angle π radians. Therefore we can say that the phase difference between particles 3 and 4 is π radians. Particle 5is in equilibrium position and particle 6 is at the upper extreme. This means that particle 6 is one-quarter of a vibration ahead of particle 5, or the phase difference between them is π /2....
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- Fall '10