Energy per second transferred by the resultant wave

[desmond iking]

Homework Statement

the energy transferred per second by a progressive waves is directly propotional to the square of its amplitude, if two waves are in phase and superposed, the energy per second transferred by the resulatant wave propotional to A.) the sum of amplitude. B). The diffrenece of the amplitudes.

Homework Equations

The Attempt at a Solution

my ans is A. since when two waves superposed at a pointy, the resultant displacement is vector sum of individual displacement of two waves. BUT the ans given is B .

 

[Simon Bridge]

So how would you go about proving that you are right?
Maybe a mathematical treatment?

 

[desmond iking]

So how would you go about proving that you are right?
Maybe a mathematical treatment?

i am not saying i am right. just based on the reason the resultant displacement is vector sum of individual displacement of two waves. i chose A. so am i correct?

 

[dauto]

Neither A) nor B) seem correct to me. May be I misunderstand the question?

 

[Simon Bridge]

i am not saying i am right. just based on the reason the resultant displacement is vector sum of individual displacement of two waves. i chose A. so am i correct?

You have said that the model answer says the correct answer is (B) - you did not put that, so you were marked incorrect.
The question only arises if you suspect the model answer is wrong - so you were marked down unfairly.

Therefore, your problem is that you need to find some way to show that the model answer is incorrect, or, failing that, to confirm the model answer is indeed correct.

Your reasoning, how you would go about showing that you are correct, or that they are correct, or whatever, will help us figure out how best to help you.

I'll start you off - you are told that the energy per second of a wave is proportional to the amplitude squared. You write this is as: $$P\propto A^2$$

You are told that two of these waves are in phase - so what is the amplitude of the combined wave?
If the combined wave obeys the same power-amplitude relationship as individual waves, what is the rate of energy transfer for the combined wave?

Please bear in mind that me just telling you if you are correct amounts to telling you the answer - which is against the forum rules.

 

[Simon Bridge]

@Dauto: I could make a case either way - the question seems to be from the UK A-level curriculum referring to mechanical traveling waves. Students will have been expected to use their understanding of the coursework to answer the question - which is why it seems a bit incomplete and glib. Either that or we don't have the full text here.

I want to see OPs reasoning before giving away the answer.