The displacement of a plane progressive wave in a medium, travelling towards positive x -axis with velocity 4 m / s at t = 0 is given by y = 3 sin 2 π ( − 3 x ) . Then the expression for the displac

Question

The displacement of a plane progressive wave in a medium, travelling towards positive x -axis with velocity 4 m / s at t = 0 is given by y = 3 sin 2 π ( − 3 x ​ ) . Then the expression for the displacement at a later time t = 4 sec will be

TestHub · Accepted Answer

Hint : Let y = 3 sin [ ω t − kx ] y = 3 s i n ( − k x ) at t = 0 ​ k = 3 2 π ​ v = k ω ​ 4 = 2 π /3 ω ​ ⇒ ω = 3 8 π ​ ∴ y = 3 sin [ 3 8 π ​ t − 3 2 π ​ x ] ∴ t = 4 y = 3 sin [ 3 8 π ​ × 4 − 3 2 π ​ x ] = 3 sin 2 π [ 3 − x + 16 ​ ] y = 3 sin [ 2 π ( − 3 x − 16 ​ ) ] ​

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