# Wave Interference question

1. Sep 17, 2014

### Monster007

If I have two waves travelling in opposite directions as shown in the attached image... After 30 seconds what will the waveform look like?

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2. Sep 17, 2014

### olivermsun

Are there any (length) units or any other explanation to go with the picture? Are these supposed to represent two waves in the same string?

3. Sep 17, 2014

### Monster007

No no measurements they just sit under each other... they are assumed to be in same medium though. It says they meet after 30 seconds. what is the expected waveform

4. Sep 17, 2014

### Monster007

So I'm assuming they meet after 30 seconds in phase? Because one travels twice as quick as the other which means they will meet end to end as drawn?

5. Sep 17, 2014

### olivermsun

Are you familiar with "wave superposition"?

6. Sep 17, 2014

### Monster007

Yes, but i'm wondering what actually happens, as in.... I'm assuming they will superimpose but im not certain for how long and what the resulting waveform will actually be... I know where peaks add I'll get twice the amplitude, but where will they add etc

7. Sep 17, 2014

### olivermsun

Well, it depends what you mean by the waves "meet" after 30 seconds. Do they just meet (head-to-head) or are they exactly on top of each other? In the first case you just draw them head-to-head. In the second you superpose them.

The waves are propagating, so they will move past one another… hence they will superpose at every different position, but only for an instant at each position.

If you do a quick Google search for "wave superposition" it turns up a lot of good diagrams and videos of two waves meeting in just the way you are describing.

8. Sep 17, 2014

### Monster007

well im assuming that after any time the bottom wave will have gone through exactly 2 times as many wavelengths as the top wave as its frequency is twice as much (velocity is, and wavelength is same) but this should result in the waves meeting head to head.... so will they constructively interfere?

9. Sep 17, 2014

### olivermsun

If it's a wave in a string, the waves will propagate completely unchanged. So you literally slide the two waves past each other and add them together to get the total wave at each moment in time.