Chapter 14, Problem 76A

To determine

To Sketch: The result for each of the three cases.

Explanation of Solution

Introduction:

According to the superposition principle, two waves moving in opposite direction get superimpose to each other and form a new wave which could have greater, lesser or zero amplitude.

Let, the amplitude of each wave be $A$ .

Case: 1

The amplitude of new wave gets double when two waves of same amplitude superimpose to each other in same phase i.e. crest of one wave superimpose to the crest of another wave or vice versa.

Therefore, the sketch:

  

Case 2:

When a crest lands on a trough of the same magnitude, they cancel each other, and no displacement occurs.

If $A$ is the amplitude of each wave, then the amplitude of resulting wave will be $A-A=0$

Therefore, the sketch:

  

Case 3:

One can see from the calculation that the second wave’s amplitude is double that of the first. If the first wave’s amplitude is $A$ , then amplitude of the second wave is $-2A$ In this case, negative sign indicates that the displacement is in the downward direction. Then the amplitude of the resulting wave will be $A-2A=-A$ .

Therefore, the sketch:

  

Conclusion:

Hence, the sketches of resultant waves for all three cases is shown.