General Physics II
General Physics II PHYS 408
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This 5 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 9 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 6 Sound Waves Part I Chapter 18 59 Sound Intensity The intensity of sound is given by the average rate at which energy ows through an area per time and per unit area 1 5 A 11 P a Where P is the power dt We can rewrite this check the math in the book as 1 2 2 I 79 Sm 12 P L vmz 2 This should look familiar Remember the rate of energy from down a string is avg 2 l ym Since the intensity of the wave drops like the area the intensity at a certain distance r would be PS 47W2 13 where P is the power of the source So the intensity follows an inverse square of the distance to the source When you are twice as far removed the intensity is four times less Decibel Scale Our perception of sound is different from eq 110 or 1 11 Our hearing is more like the sound level of a sound than the intensity The sound level is defined by a 10dB1ogIi 0 14 712 2 Where 0 10 Wm is the standard reference intensity which corresponds to a sound level of 0 about the smallest noise we can perceive Note that because of the log part of this equation the intensity increases very rapidly as we go up in sound level 15 242003 Musical Pipes All the wind instruments make use of some vibrating element a reed for a saxophone or hobo lips for a trumpet a small aperture for a ute and a pipe to create a standing wave of a speci c frequency Several con gurations are possible Both ends closed which is like a vibrating clamped string we ve done that already one end open or two ends open Sound in a pipe with two ends open will have 2 antinodes at the ends It look like the gure Note that the green lines are a representation of the displacement of F71 4 the air molecules It is too dif cult to draw them as in a so we make 3 5 g i1 the representation like in b A A From the gure you can immediately see that the fundamental mode has 7F2L From the next picture you can easily derive that the next harmonic 2n01 harmonic would be when 7FL In general fl jly quot1121314 A 2 L 15 which will give you all the possible frequencies The pipe with one end open is a little trickier The fundamental n 1 IA4L mode is 7F4L the next possible harmonic is at 9F4L3 Since the frequency ofthis harmonic is 3 times that ofthe fundamental quot3 4 mode we call this the 3rd harmonic The 2 01 harmonic is not a possible for such a pipe In general quot5 mm f111 n1357 4 L 16 where you have to remember that n is odd BEATS When two sounds or waves on a string or any other wave of almost the same frequency mix interfere you hear a funny wowwowwow sound This is due to the beats of the two waves Let s add two sound waves with the same amplitude and almost the same frequency s1 sm cosa1t s2 sm cosa2t ss1s2 sm cosa1tcosazt 17 We can rewrite the resulting wave with the cosines identity cosa cos 2cos zigjcosg 2 2 2 2 and if we choose iw1 wzgt wiwlwz wecanwrite a 25 242003 s2sm cosw tcoswt 18 cosa t Now if f1 and f2 are almost the same frequency then the term oscillates much l slower than the 005wt and the result is that the 2s cosw t part behaves like an amplitude The beat frequency is the oscillations of this amplitude not the cos term so see gure bem20quot0 1 0 2 ffi f2 19 06 04 02 0 02 04 06 tsec You can see from the gure how the green and the red wave undergo constructive interference in one part and destructive interference in another 35 242003 Doppler When a race car drives by you first hear a high pitched whine which drops signi cantly when the car is passed This is the Doppler effect In formula form f fvivD V VS 110 Where f is the observed frequency and f the emitted frequency The variable v is the speed of sound V the speed of the source and VD the speed of the detector both velocities are with respect to the air The book derives this in two steps but let us do it in one When both source and detector are not moving the source oscillating with a frequency sets up a sound wave that travels v k away from the source with a wavelength A L 12 111 The waves travel to the detector D and there set the receiver to oscillate with a frequency fd that is given by V f 1 112 When both the source and the detector are moving with respect to the air the velocities need to be adjusted The source v 9 vi moves in the direction of the wave so the velocity at which the waves leave the source is v vs The detector moves towards the waves so the velocity of the incoming waves is vvd Using this in equation 111 and 112 and substituting 111 for the 7 in 112 we get Viv 2391 x a d f fd 239 fdzfsvivd VVS 1 13 Note that the sign is quite important 45 242003 Shock Waves What happens when an object that produces sound goes faster than the speed of sound We get a shock wave This can actually also happen with light when a particle moves faster than the speed of light in the medium This is called the Cherencov effect A characteristic of a shockwave is the opening angle of the shock wave front the boom This is easily derived from the gure using the green distance that the sound has traveled and the red distance that the object traveled sin 6 V t1 VJ Vs 114 V5 The ratio is called the Mach number and indicated how much faster than the speed of sound the object is moving 55 242003
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