Wave motionHard
Question
A wave represented by y = 2 cos (4x - πt) is superposed with another wave to form a stationary wave such that point x = 0 is a node. Then the equation of other wave is :-
Options
A.y = 2 sin (4x + πt)
B.y = - 2 cos (4x - πt)
C.y = - 2 cos (4x + πt)
D.y = - 2 sin (4x - πt)
Solution
For stationary waves, two waves must go in opposite direction,
y = y1 + y2
= 2 cos (4x - πt) - 2 cos (4x + πt)
= 2.2 sin 4x sin πt
At x = 0 node is formed i.e. y = 0
y = y1 + y2
= 2 cos (4x - πt) - 2 cos (4x + πt)
= 2.2 sin 4x sin πt
At x = 0 node is formed i.e. y = 0
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