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Unformatted text preview: 1 Lesson 5.4 Harmonic Sound Waves Lesson Objectives: At the end of this lesson students will be able to (i) apply the concepts of harmonic waves to describe sound waves and explain common phenomenon such as Doppler effect and intensity level. (ii) solve problems using the concepts of harmonic sound waves. Sound is a form of energy transfer which needs a material medium for propagation. Sound is propagated through solids, liquids and gases in the form of longitudinal waves. In a longitudinal wave, the direction of particle vibration is the same as the direction of propagation of the wave. Sound is produced by vibrating objects. A vibrating object has an equilibrium position and two extreme positions as shown in the figure below. left extreme right extreme comprression rarefaction Fig. 1 As the vibrating object move from the extreme left to the extreme right, the particles of the medium are pushed right and a region of high density called compression is created. This region of high density is propagated to the right. As the vibrating object moves from right to left the particles of the medium are pulled back, creating a region of low density called rarefaction . The particles of the medium are thus set into simple harmonic vibration. When the particles vibrate in the direction of the wave, they are in a region of compression and when the particles vibrate in a direction opposite to the direction of propagation of the wave, they are in a region of rarefaction. The compression and rarefaction in a longitudinal wave are analogous to the crest and trough in a transverse wave. The vibrations of particles at the center of a compression differ in phase by with those at the center of a rarefaction. The wave length of a longitudinal wave is the distance between consecutive compressions or consecutive rarefactions. 2 1. Speed of sound waves . Speed of sound waves in a medium depends on how fast particle vibrations are transmitted through the medium. It largely depends on the elastic properties of the medium. Speed of sound waves through water depends on the bulk modulus of water while the speed of sound through steel depends on its Young's modulus. The speed of sound in air depends on the pressure and density of air and is given by the equation: P v = ..1 where P is the atmospheric pressure and is the density of air. is a constant and has a value 1.4 for air. Since the value of P/ depends on temperature, the speed of sound in air varies with temperature. An approximate relation connecting v o ,speed of sound at 0 o c, and v t , speed of sound at t o C can be written as: v t = v o + 0.6t ..2 Example 1 : Find the speed of sound in air at STP Solution: The normal atmospheric pressure P = 1.013 10 5 Pa The density of air 0 o C = 1.29 kgm-3 ....
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- Fall '10