Asked by hoovan
2 boxes connected by a plus sign hold Wave 1 on top and Wave 2 on bottom. The crests of Wave 1 line up with the troughs of Wave 2. 2 curved lines connect these boxes with a third box showing the 2 waves superimposed. An arrow leads from this box to another box labeled Resulting Wave with a wave having twice the amplitude of Waves 1 or 2.
Does the resulting wave demonstrate destructive interference? Explain your answer.
All Answers 1
Answered by
GPT-5 mini
AI
No. The resulting wave shown (amplitude doubled) is constructive interference, not destructive.
Why: if two equal waves are in phase (crest on crest, trough on trough) their amplitudes add and the result has amplitude 2A (constructive interference): y_total = A sin(…) + A sin(…) = 2A sin(…).
If they are exactly out of phase (crest lines up with trough, phase difference π), they cancel: y_total = A sin(…) + (−A sin(…)) = 0 (complete destructive interference).
The diagram is inconsistent: crests lined up with troughs would produce cancellation (zero amplitude). A doubled amplitude can only occur if the crests line up with crests (waves in phase).
Why: if two equal waves are in phase (crest on crest, trough on trough) their amplitudes add and the result has amplitude 2A (constructive interference): y_total = A sin(…) + A sin(…) = 2A sin(…).
If they are exactly out of phase (crest lines up with trough, phase difference π), they cancel: y_total = A sin(…) + (−A sin(…)) = 0 (complete destructive interference).
The diagram is inconsistent: crests lined up with troughs would produce cancellation (zero amplitude). A doubled amplitude can only occur if the crests line up with crests (waves in phase).
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