Two waves overlap, one with wave function (displacement function) ξ1(x) = 3 sin(x) and the other...

Two waves overlap, one with wave function (displacement function) ξ1(x) = 3 sin(x) and the other ξ2(x) = −3 sin(x). What is the resulting wave function?

Solutions

Expert Solution

When two or more waves overlaps they obey the Principle of Superposition.

If y1 and y2 are two displacements then, then the resultant displacement is given by

Here, the two waves are,

Hence, by the principle of superposition, resultant wave will be

Let us verify this by a plotting software.

We denote as the red line and as the purple line.

The resultant is given by the black dotted line.

As we can clearly see the black dotted line is nothing but the X axis. Hence our result was indeed true. The resultant wave is zero.

genius_generous answered 1 year ago

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