InterviewSolution
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InterviewSolution
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A wave is given by the equation ` y = 10 sin 2 pi (100 t - 0.02 x) + 10 sin 2 pi (100 t + 0.02 x)` Find the loop length , frequency , velocity and maximum amplitude of the stationary wave produced. |
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Answer» Correct Answer - maximum amplitude `20 units ` wave velocity is `5000 units`. Frequency `100 units` loop length is `25 units` We know the equation of a stationary wave is given by `y = A sin [ ( 2 pi)/( lambda) ( vt - x)] + A sin [ ( 2 pi)/(lambda) ( vt + x)]` `= 2 A cos ( 2pi x)/( lambda) sin ( 2pi v t)/( lambda)` ` = R sin ( 2pi)/( lambda) vt` Here , `R = 2 A cos (2 pi x// lambda)` is the amplitude of medium particle situated at a distance `x`. The given equation can be expressed as `y = 10 sin [( 2 pi)/( 50) (5000 t + x)]` ` = 2 xx 10 cos (( 2pi x)/( 50)) sin (( 2pi)/(50) 5000 t)` Comparing it with standard equation of stationary wave , we get wavelength `lambda = 50 units` Wave velocity ` v = 5000 units` Thus amplitude `R = 2 xx 10 cos ( 2 pi x)/( 50)` and maximum amplitude `R_(max) = 2 xx 10 = 20 units` Frequency `= (v)/( lambda) = ( 5000)/(50) = 100 units` And loop length is `(lambda)/(2) = (50)/(2) = 25 units` |
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