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Lesson 5.4 Harmonic Sound Waves

# Lesson 5.4 Harmonic Sound Waves - Sound Waves Sound is a...

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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 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. left extreme right extreme comprression rarefaction 1

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left extreme right extreme comprression rarefaction 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. 3

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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 π with those at the center of a rarefaction. The wave length of a longitudinal wave is the distance between consecutive compressions or consecutive rarefactions. λ left extreme right extreme comprression rarefaction http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html 4
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 . 5

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The speed of sound in air depends on the pressure (P) and density ( ρ ) of air and is given by the equation: P v γ ρ = Since the value of P/ ρ depends on temperature, the speed of sound in air varies with temperature. v t = v o + 0.6t For air, γ has a value 1.4 6
Example 1 Find the speed of sound in air at STP The normal atmospheric pressure is: o P v γ ρ = P = 1.013 x 10 5 Pa ρ = 1.29 kgm -3 5 -3 1.4 1.013 10 Pa 1.29 kgm × × = = 332 ms -1 7

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Determine the speed of sound in air at 30 o C. Example 2 = 350 ms -1 8
Harmonic Sound Waves If s(x,t) is the displacement of a particle at any time t , and s o , the displacement amplitude, then the harmonic wave equation is: s(x,t) = s o sin(kx – ϖ t) Since the displacements of the particles cause pressure variations in the medium, it is more

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