Why do waves need to be in phase for constructive interference to occur?

[maccha]

So I know that for constructive interference to occur, in phase waves must be separated by a distance 2 pi. What I'm confused about, though, is what if the point they interfere at is separated by a distance 2 pi, but isn't where their crests meet? Like what if one speaker is one wavelength behind the other, but they both start off at zero amplitude, so wouldn't that point where they meet still be zero? Thanks for the help.

 

[denverdoc]

I think you mean to say that in order for constructie...the differences in path length must be an integer multiple of the wavelength, could be 1, or 100 so long as they arrive in phase.

And yes zero plus zero is zero, just as the point of maximum will be two times the individual. Is this any help?

 

[maccha]

Yes sorry that is what I meant. But don't they just interfere at one point, so if it's not at the troughs wouldn't maximum interference not always occur for a distance of one wavelength?

 

[denverdoc]

When they are exactly in phase (lined up so the crests are arriving simultaneously), all points add and only the zeros (crossing point) don't get bigger. When exactly antiphase, 180 degrees apart, there will be no sound heard at the listening point--imagine a point size microphone. Anywhere else you will hear sound. Bass is especially prone to these issues, but if you were to do an exact frequency plot with a high quality mike using a signal generator, the graph looks like the teeth of a comb for just this reason: at any distance some frequencies will be perfectly in phase, others antiphase and most in between.

 

[Adjuster]

Perhaps it may help you understand if you think about what happens as time continues.

The instantaneous wave amplitude may be zero at the point in time and space you are considering, but as time goes on it will continually vary between its crest values.

 

[Adjuster]

Perhaps it may help you understand if you think about what happens as time continues.

The instantaneous wave amplitude may be zero at the point in time and space you are considering, but as time goes on it will continually vary between its crest values.

 

[maccha]

Hm, I understand it when you think of it over time for two speakers on the same axis facing the same direction. But I don't understand when it's two speakers facing each other. I have an example that asks to find loud spots a person will hear when walking between two speakers facing each other (in phase). Why don't they constructively interfere the entire time? I don't know, I think I'm thinking about this completely wrong but I'm imagining two waves starting off at the same point and overlapping the entire time.

 

[denverdoc]

Because as you walk towards one speaker and away from the other the path length from the two changes. It is all about the difference in path lengths. If the difference in pathlengths is off by a 1/2 wavelength, you have destructive interference, off by one complete wavelength, the sounds add. In between is in between.

 

[maccha]

Okay so if it's a complete wavelength they'll add- but how do we know they'll interfere at a point of amplitude A and not a point 0 on their wave? Sorry I know I'm going in circles.

 

[denverdoc]

You really should just google the question and see with your own eyes how it works. We are talking about a collision of two "forces"--if the surges coincide you have constructive interference (additive) or if a trough and crest collide, you have zilch, but everything between these extremes is partial addition or subtraction.

 

[maccha]

Okay thanks for the help. One last quick question. Don't two waves of the same frequency traveling in opposite directions produce a standing wave? Why wouldn't this produce a standing wave?

 

[denverdoc]

Damn straight. Put two big facing woofers in a big room and walk slowly from one to the other. This isn't some BS effect. In most rooms you can feel a huge difference as you go from null to peak (destructive interference vs constructive), It is not sudden.