TBR Physics Section 5, Passage 6, Question 40. Please help!!!

[4563728]

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The passage says, "Studies show that 2 waves of differing wavelengths and amplitudes could pass through each other without any distortion in their wavelength or amplitude."
Question 40 then asks, "How can it be explained that when two deep-water ocean waves pass through the same point simultaneously, the water level neither rises or drops?"

A. The wavelengths do not change when two waves pass through one another.
B. The wavelengths do change with 2 waves pass through one another
C. Two passing waves must have gone undergone perfectly constructive interference at that point.
D. Two passing waves must have gone undergone perfectly destructive interference at that point.

I picked option A, that basically repeats the statement in the passage, "studies show that two waves of differing wavelengths could pass through each other without any distortion in the wavelength or amplitude," but that wasn't the correct answer. Instead it says the two waves had undergone perfect destructive interference. But doesn't this answer completely negate what is said in the passage? The explanation only confused me more and I would really appreciate any help on the problem. Thanks!

 

[QuinnTheEskimo]

The passage says, "Studies show that 2 waves of differing wavelengths and amplitudes could pass through each other without any distortion in their wavelength or amplitude."
Question 40 then asks, "How can it be explained that when two deep-water ocean waves pass through the same point simultaneously, the water level neither rises or drops?"

A. The wavelengths do not change when two waves pass through one another.
B. The wavelengths do change with 2 waves pass through one another
C. Two passing waves must have gone undergone perfectly constructive interference at that point.
D. Two passing waves must have gone undergone perfectly destructive interference at that point.

I picked option A, that basically repeats the statement in the passage, "studies show that two waves of differing wavelengths could pass through each other without any distortion in the wavelength or amplitude," but that wasn't the correct answer. Instead it says the two waves had undergone perfect destructive interference. But doesn't this answer completely negate what is said in the passage? The explanation only confused me more and I would really appreciate any help on the problem. Thanks!

Destructive interference means that the crest of one wave hits the trough of a second wave. As a result, they cancel each other out and water level stays flat at the point of interference.

It doesn't have to do with wavelength.

 

[4563728]

I understand the concept behind destructive interference but what I don't understand is why the statement in the passage contradicts the correct answer choice. Aren't they saying the exact opposite things?

 

[QuinnTheEskimo]

I understand the concept behind destructive interference but what I don't understand is why the statement in the passage contradicts the correct answer choice. Aren't they saying the exact opposite things?

No. They are saying that after the waves interfere, they continue on their merry way with no change in amplitude or wavelength. But at the point of interference, they definitely interact.

 

[4563728]

This may be totally wrong, but wouldn't two ocean waves, if they are at the same point at the same time, actually undergo constructive interference? Maybe my intuition is wrong but when I picture one wave with another wave coming up behind it and passing through the first wave, i would imagine they would become larger, right?

 

[QuinnTheEskimo]

This may be totally wrong, but wouldn't two ocean waves, if they are at the same point at the same time, actually undergo constructive interference? Maybe my intuition is wrong but when I picture one wave with another wave coming up behind it and passing through the first wave, i would imagine they would become larger, right?

You are thinking of two crests interfering. if a crest (high point) and trough (low point) interfere, they cancel each other out.

 

[4563728]

But where in the question does it specify whats interfering? They don't say if its two crests or a crest and a trough...

 

[4563728]

Thanks for the help, by the way! 🙂

 

[QuinnTheEskimo]

But where in the question does it specify whats interfering? They don't say if its two crests or a crest and a trough...

It says two waves interfere and cause the water to remain level. This must either be a) destructive interference, or b) they are interacting at a node. Node is not an option, so it has to be destructive interference by process of elimination.

 

[4563728]

Oh, that makes so much sense! Thank you so much!! One last question though, it what context would the answer 'interacting at a node'?

 

[QuinnTheEskimo]

Oh, that makes so much sense! Thank you so much!! One last question though, it what context would the answer 'interacting at a node'?

Interacting at a node would just be another possible option, but they don't offer it in the choices. The amplitude at the node is zero, by definition. So if 2 nodes meet, the water level will not change.

 

[4563728]

Right, that makes perfect sense. Thanks!!