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A progressive wave of frequency 500 Hz is travelling with a velocity of 360 m/s.How far apart are two points 60^@ out of phase ? (ii)Does the speed of a plane-progressive wave depend on the amplitude ? (iii)The equation of a progressive wave is represented by Y=A sin^2 (kx-omegat). Find its amplitude and frequency (iv)Which of the following equations represents a wave travelling along positive y-axis?(a)x=5 sin (2y-6t)(b) y=6sin (7x-5t) (c ) y=10 sin (6y) cos (8t) |
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Answer» Solution :Phase difference `PHI=(2pi//lambda)` x path difference `RARR pi/3 =(2pi)/lambdaDeltax` `rArr Deltax=lambda/6=V/(6f)`=12 cm (ii) No (iii)The given equation can be WRITTEN as Y=(A/2)[1-cos (2kx-`2omegat`)] Amplitude of this wave is (A/2) and frequencyis `(omega//pi)`, where as angular frequencyis `2omega`. (iv)The most general equation of a wave travelling ALONG y-axis will be `x=A sin [(ky - omegat) pm phi)]`comparing this with the given equations we find that the first equation i.e. x=5 sin (2y-6t) represents a wave travelling along positive y-axis . |
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