Asked by Anonymous

Consider this image of a wave.

A graph with time in second on the x axis from 0 to 8 and amplitude on the y axis from 2 to 2. The wave starts at the origin and the trough goes down to 2, back up through 1 s and all the way up to .7 before going back down to .2 on the other side of the x axis. It is a repeated pattern with on trough and 3 crests with different amplitude.
Which wave would cause destructive interference at every point of the wavelength and completely cancel out the wave?

A graph with time in second on the x axis from 0 to 8 and amplitude on the y axis from 2 to 2. The wave starts at the origin and the trough goes up to .8, back down through .75 s and all the way down to 2 before going back up to 2 on the other side of the x axis. It is a repeated pattern with on trough and 3 crests with different amplitude.
A graph with time in second on the x axis from 0 to 8 and amplitude on the y axis from 2 to 2. The wave starts at the origin and the trough goes down to 2, back up through 1 s and all the way up to .7 before going back down to .2 on the other side of the x axis. It is a repeated pattern with on trough and 3 crests with different amplitude.
A graph with time in second on the x axis from 0 to 8 and amplitude on the y axis from 2 to 2. The wave starts at the origin and the trough goes down to .6, back up through 1s and all the way up to .6 before going back down to .4 on the other side of the x axis. It is a repeated pattern with on trough and 3 crests with different amplitude.
A graph with time in second on the x axis from 0 to 8 and amplitude on the y axis from 2 to 2. The wave starts at the origin and the trough goes down to 2, back up through 1s and all the way up to .7 before going back down to .2 on the other side of the x axis. Then back up to .3 on the other side of the x axis. The pattern repeats itself but flipped on the x axis

All Answers 1

Answered by GPT-5 mini AI
Destructive interference everywhere requires the second wave to be exactly the negative of the first: y2(t) = −y1(t) for every t (same shape and amplitudes, 180° phase shift).

That is the wave which is the original pattern flipped across the x‑axis — the last option ("pattern repeats itself but flipped on the x axis"). The others have different amplitudes/shape so they would not cancel everywhere.