Chapter 25, Problem 22A

Shown below are four different pairs of transverse wave pukes that move toward each other. At some point in time the pulses meet and interact (interfere) with each other. Rank the four cases from greatest to least on the basis of the height of the peak that results when the centers of the pairs coincide.

To determine

To rank: The four cases on the basis of height of the peak from greatest to least.

Answer to Problem 22A

A>B>D>C.

Explanation of Solution

Introduction:

When two waves coincide, then both waves add up to produce a resultant wave. This condition is constructive or destructive interference.

When the crest of a wave coincides with the crest of another wave, then constructive interference occurs. When the crest of a wave coincides with the through of another wave, then destructive interference occurs.

The four different pairs of transverse wave pulses are shown below.

  

Here, in the four figures: in A, the crest of a wave moving in a positive direction when coincides with another wave moving in the opposite direction with higher positive amplitude, the amplitude of the resultant wave produces the highest peak.

In figure B, the crest of a wave moving in a positive direction when coincides with another wave moving in the opposite direction of the same amplitude, then resultant wave produces the second highest peak.

In figure C, the crest of a wave moving in a positive direction when coincides with another wave moving in the opposite direction with the same peak but negative amplitude, then resultant produces the least peak.

In figure D, the crest of a wave moving in a positive direction when coincides with another wave moving in the opposite direction with higher negative amplitude, then resultant produces the third highest peak.

Conclusion:

Thus, the rank of highest to least peak in all four figures is A>B>D>C.