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Unformatted text preview: Discussion # 22 – Mechanical Waves I Q15.9 : Why do you see lightning before you hear the thunder? A familiar rule of thumb is to start counting slowly, once per second, when you see lightning; when you hear the thunder, divide the number you have reached by 3 to obtain your distance from the lightning in kilometers (or divide by 5 to obtain the distance in miles). Why does it work? Q15.15: A long rope with mass m is suspended from the ceiling and hangs ertically A wave pulse is produced at the lower end of the rope and the vertically. A wave pulse is produced at the lower end of the rope, and the pulse travels up the rope. Does the speed of the wave pulse change as it moves up the rope, and if so, does it increase or decrease? E15.12: (a) Show that equation may be written as . (b) Use y(x,t) to find an expression for ( ) , c o s x y x t A t v ω ⎡ ⎤ ⎛ ⎞ = − ⎜ ⎟ ⎢ ⎥ ⎝ ⎠ ⎣ ⎦ ( ) ( ) 2 , c o s y x t A x vt π ⎡ ⎤ = − ⎢ ⎥ ⎦ λ ⎣ ⎦ the transverse velocity v y of a particle in the string on which the wave travels. (c) Find the maximum speed of a particle of the string. Under what circumstances is this equal to the propagation speed v? Less than v? Greater than v? (a) ( ) ( ) 2 2 , cos cos 2 cos 2 2 cos x f x x v y x t A t A ft A t A x vt v π π ω π π π ⎡ ⎤ ⎛ ⎞ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ = − = − = − = − ⎜ ⎟ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎠ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ v v λ λ λ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎝ ⎠ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (b) ( ) ( ) ( ) ( ) , 2 2 2 2 , sin sin y y x t v v x t A x v t v A x v t t π π π π λ λ λ λ ∂ ⎡ ⎤ ⎛ ⎞ ⎡ ⎤ = = − − − = − ⎜ ⎟ ⎢ ⎥ ⎢ ⎥ ∂ ⎣ ⎦ ⎝ ⎠ ⎣ ⎦ ⎣ ⎦ ⎝ ⎠ ⎣ ⎦ (c) max 2 y v v A π λ = This will equal the propagation speed v when 2...
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This note was uploaded on 09/13/2011 for the course PHYSICS 140 taught by Professor Evrard during the Spring '07 term at University of Michigan.
 Spring '07
 Evrard
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