Wave constructive and/or destructive interference question

[kirsten_2009]

Homework Statement

https://portal.utoronto.ca/courses/1/Fall-2014-PHY100H5-F-LEC0101/ppg/quiz%2061016132114/f1q2g1.jpg

The figure shows two sets of water waves, created by two sources labeled "A" and "B." The solid half-circles represent wave crests from A, and the dashed half-circles represent wave crests from B. Suppose that individual wave crests from either source A or source B alone are 5 mm above the level of the undisturbed water. Then the displacement of the water [above or below the level of the undisturbed water] at the point marked "x" [with the arrow pointing toward it] is

A.) -10 mm.
B.) 0 mm.
C.) +5 mm.
D.) +10 mm.
E.) -5 mm.

Homework Equations

[/B]
N/A

The Attempt at a Solution

I think it would be E.) -5mm because if we are just taking one wave set alone (either A or B) then there would be no interference from the other wave set and if the displacement from rest is 5mm then the opposite displacement must be equal in magnitude...? But I don't actually know...I'm just thinking it out...would you please correct me if I'm wrong? Thanks in advance!

 

[RUber]

I cannot see your figure. Could you check to see that it was attached properly?

 

[RUber]

Although I cannot see the picture, here is a hint. You can add the wave effects together. So, if x lies on a wave crest from A, (+5mm), and the midpoint between crests from B (-5mm), then the total displacement at x would be 0.

 

[kirsten_2009]

Hello,

Yes, unfortunately there was no way to upload the image but thank you for your help...it actually helped me get the answer! :)

 

[HalfLostAndSearching]

Your reasoning is correct! When two waves interfere, they can either constructively or destructively interfere. Constructive interference occurs when the wave crests from two sources align and add together, resulting in a larger displacement. Destructive interference occurs when the wave crests from two sources are out of phase and cancel each other out, resulting in a smaller displacement. In this case, the two wave sets are out of phase, leading to destructive interference at point "x". Therefore, the displacement would be in the opposite direction and have the same magnitude, resulting in a displacement of -5 mm.