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Unformatted text preview: We now let x x- vt to have a wave traveling to the right. I.e., f ( x, t ) = y m sin[ k ( x- vt )] = y m sin( kx- kvt ) = y m sin( kx- t ) (1) where := kv , v = k , and is the angular frequency. At any x , the motion is a simple harmonic motion. Let t t + 2 . Then, f ( x, t + 2 ) = y m sin[ kx- ( t + 2 )] = y m sin( kx- t- 2 ) = y m sin( kx- t ) (2) therefore, T = 2 is the period. Recall that f = 1 T = 2 = 2 f . v = k = 2 k 2 = T so that the wave travels a distance over a time T . Another view: Take a snapshot in time: so that k = 2 . 4 Snapshot in space: so that T = 2 . String Velocity (in the transverse case) String Velocity: Not the same as wave velocity! u ( x, t ) = f t x =const (3) Because were looking at how fast each material point is moving: the velocity here is of a specific piece of the string. If f ( x, t ) = y m sin( kx- t ) then u ( x, t ) = f t =- y m cos(...
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This note was uploaded on 07/19/2011 for the course PH 113 taught by Professor Liorburko during the Spring '09 term at University of Alabama - Huntsville.
- Spring '09