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hw19 - Physics 21 Fall 2004 Solution to HW-19 Problem 1 A...

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Physics 21 Fall, 2004 Solution to HW-19 Problem 1 A wave on a string travels at 5 m/s toward the right (labeled the positive x direction). The transverse displacement of the string at a point arbitrarily labeled x = 0 is observed to be y 0 ( t ) = 0 . 03 e 0 . 6 t cos(50 t ) , where t is in seconds and y is in meters. (a) What is the mathematical expression for the traveling wave on the string as a function of x and t ? (b) Answer part (a) for a wave moving toward the left rather than toward the right. Replace t by t ± x/v , using the upper (lower) sign for propagation to the left (right): y 0 ( x, t ) = 0 . 03 exp 0 . 6 t ± x v cos 50 t ± x v For v = 5 m/s, y 0 ( x, t ) = 0 . 03 exp [ 0 . 6 t 0 . 12 x ] cos [50 t ± 10 x ] . Problem 2 What is the frequency of yellow light with a wavelength of 5 . 9 × 10 7 m in empty space? λf = c f = c/λ = 3 × 10 8 5 . 9 × 10 7 = 5 . 1 × 10 14 Hz Problem 3 The mathematical expression for a traveling wave on a string is given by y ( x, t ) = 0 . 03 sin(40 πt + 8 πx ) where x and y are in meters, t is in seconds, and x 0. (a) In what direction does the wave propagate?
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