A wave on a string meets with another wave producing a node at . Then the equation of the unknown wave is:
- (A)
- (B)
- (C)
- (D)
The Correct Option is B
Solution and Explanation
Given:Equation of wave, ......(i)Since the coefficient of is negative in the above wave equation, it suggests that the wave is traveling in a positive direction. The other wave must travel in the opposite direction to form a node.Let the two possible equations of waves travelling in negative direction be......(ii)and.......(iii)Using the propertyIf waves (i) and (ii) superimpose, the net displacement isSimilarly,So, if waves (i) and (iii) superimpose the net displacement isSince at node, displacement so Therefore, eq. (iii) satisfies the property of a node at .So, the equation of the unknown wave isHence, the correct option is (B).
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