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Unformatted text preview: Tutorial ODWE: One-Dimensional Wave Equation 5. Solutions to Exercises Exercise 1 . Transverse waves have the disturbance perpendicular to the direction of propagation of the disturbance. Dont confuse the wave motion with the propagation. Exercise 2 . If the frequency is f; then in an amount of time, = 1 =f , a length, , of wave passes a given point. Thus, the speed of its passing is v = = (1 =f ) = f: Exercise 3 . The amplitude in the expression A cos 2 ( x t ) + remains the same (i.e., the wave form moves in the direction of propagation) when x varies with time so as to keep the argument of the cosine function a constant. Thus, considering x to be a function of time, d dt 2 ( x t ) + = 2 ( dx dt ) = 0 = ) dx dt = + v: The positive sign means a velocity in the positive x direction, i.e., towardsthe right. If the argument were 2 ( x + t ) = + , the constant argument condition would yield 2 ( dx dt + ) = 0 =...
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- Spring '08