General Physics II
General Physics II PHYS 408
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This 3 page Class Notes was uploaded by Cayla Kilback on Thursday October 29, 2015. The Class Notes belongs to PHYS 408 at University of New Hampshire taught by Staff in Fall. Since its upload, it has received 21 views. For similar materials see /class/231704/phys-408-university-of-new-hampshire in Physics 2 at University of New Hampshire.
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Date Created: 10/29/15
Lecture 5 Sound Waves Part I Chapter 18 14 Clari cation First something that it seems was not entirely clear from either the book or my lectures so far The question is deceiVingly simple What is the Amplitude of a wave If I give you the equation y f x ym sin 06 at dz you would know immediately to take the blue partym That is correct But what about yt x 6ym sin kx at 96 The answer is now 6 ym because the amplitude of a wave is the term that multiplies the oscillating term For a standing wave it gets even trickier because there are 2 oscillating terms one with respect to x and one with respect to I So it depends on the details of the question what the oscillating term is Let s take an example y xt4ym cosmt sinkx 11 If the question is What is the amplitude of this standing wave We mean what is the maximum of the wave for any x and any I The answer is 4 ym If the question is What is the amplitude of this standing wave at x The answer is 4ym sin2 4 I used k 2 13 1312003 Traveling Sound Waves In a traveling sound wave the particles of air move back and forth along the path of motion This movement is really very small compared to the wavelength We can write the displacement of the particles with respect to their equilibrium point as sxtsm coskx at 12 For such a wave for any wave really the wave properties k A a f T all have the same meaning as for a transverse wave When particles are displaced they must cause pressure differences The book on pages 403 and 404 shows how you derive the change in pressure from the displacement I won t repeat it here but it is a good derivation and you should know how it works They find ApxtApm sinkx at 13 and relate Apm to Sm with the equation Apm vasm Bk sm 14 The graph for such a wave looks like the Sound Wave relating SAp one here on the right Spat um Note that as the displacement goes through the equilibrium point the pressure is either at a maximum or a minimum This seems counter intuitive How do we explain it Think of the particles themselves Take the point at X30cm The particles just to the left of this point Xlt30cm have negative App displacement so they are a little bit further Pa away than usual The ones on the right Xgt30cm have a positive displacement they are also further away than usual So the pressure at X3OCII1 is at it s lowest X cm 23 1312003 Interference of Sound Waves Sound waves interfere just like 39 transverse waves do The resulting C wave displacement pressure is the 39 sum of the two or more waves you started with If you have two point sound sources SI and 1 a distance d apart emitting M the same sound frequency and Q phase these waves will interfere The pattern of interference can be calculated See the demo in Toys How is that done The phase difference of the waves at point P is given directly from the difference in path length AL L2 we find AL 27Z 7 Fully constructive interference happens when 7127239 so AL 0123 2 Fully destructive interference happens when 271 l 7239 so 2 051 52535 2 The trick is to find the AL term 2 A x2 y gt 2 L2 x2 lty gt 33 1312003 15 16 17 18
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