# Why does wave keep on travelling despite destructive interference?

I've problem here. Imagine you've a line of spheres that are attached to each other with springs. You push one sphere down hard. it drags its neighbors down and which in turn pull their neighbors and so on. You have created a wave. Now you can quantify the rate this is progressing and call it velocity of wave.

Now lets say 2 opposite waves are colliding, the sphere right in middle gets pulled down from right side and up from left. Equal opposite forces, it shouldn't move, and that's what happens. But since it hasn't moved it shouldn't pull any of its neighbors either, yet wave continues travelling through. Destructive interference didn't cancel out the wave? why.. is this model only applicable to single atoms? or something else.

rant ignore it if you want....

There is other question which was asked here and it doesn't have a suitable explanation. It just says well waves continue to travel because they have velocity. Instead of describing the reason behind phenomena it just describes model that's used to measure it. "Why is Car moving? Well because it's going 30 mph".

• it is oscillating motion but at no point either side is rotating see saw at opposite directions simultaneously. – Muhammad Umer Feb 21 '19 at 7:55
• You are describing a standing wave. Such a wave does not move. Yet your question is about travelling waves. Please make your question more clear by describing a well defined case. You will get better answers. – my2cts Feb 21 '19 at 8:31
• No, I'm not talking about standing wave. I'm saying when two waves cross each other and form destructive interference, why isn't that the end of them. Two chain reactions of opposite movement meet and continue. – Muhammad Umer Feb 21 '19 at 8:35
• – safesphere Feb 21 '19 at 8:37
• You are only thinking about half of the physics in the situation. You are talking about the kinetic energy (motion) of the spheres but you are ignoring the potential energy (stress, strain, tension, compression) in the springs. – alephzero Feb 21 '19 at 9:19

yet wave continues travelling through.

That is one way to interpret the action you're seeing. An alternate way to interpret it is that rather than passing through the center, each wave reaches the (immobile) center and reflects away from it.

If you imagine a single wave pulse reaching a certain point in a medium, as neighbors start moving, they accelerate the point in consideration. As the pulse moves forward, the neighbors ahead decelerate the point and bring it to a stop.

If you constrain the medium (such as by the end of a string being fixed to a wall), then the neighbors of that point will not be decelerated and the point will continue to vibrate. This creates a reflected wave that travels backward.

The same situation is created when the two opposite waves meet in the center. The opposite wave sets up forces that hold the center sphere motionless and the wave reflects. You get the same motion on one side that you would from setting it up with that center sphere fixed in place.

• perfect that is another mystery bothering me. Why do waves reflect? Unless molecules/atoms or fixture can be compressed they shoudn't reflect/decompress? like dropping a metal brick. there shouldn't be a bounce. so the last sphere when it tries to pull up the fixed sphere up, the fixed sphere should pull it down with equal force, causing it to just stop there. like me standing on ground if i push earth down, earth pushes me up that doens't mean i start flying. I feel problem has just shifted from two waves colliding to a wave colliding with immovable object. – Muhammad Umer Feb 21 '19 at 8:31
• @MuhammadUmer Why did you uncheck? This answer is correct. In your example, if you hit a ball against the Earth, the ball would bounce back, would it not? – safesphere Feb 21 '19 at 8:45
• @MuhammadUmer the internal forces between the floor and the falling object change the momentum of both bodies. Due to Newton's first law, total momentum is conserved. The change of momentum of the falling object is so small that the change of velocity of Earth can be neglected. In an elastic collision, the energy is conserved, so in order to conserve the energy, the falling object must conserve its velocity after the collision, this is the reason why objects bounce back. – TheAverageHijano Feb 21 '19 at 9:22
• maybe ball wasn't a good analogy. In situation, line of spheres connected by spring, last sphere is connected to immovable object. There is no colliding thus bouncing back. When last sphere pulls up immovable object, I dont see how it will cause sphere to move down, unless last sphere is connected via spring to an immovable object. does it mean wave only travel in mediums that can compress/spring like? – Muhammad Umer Feb 21 '19 at 10:29
• sorry for continued questions, but my understanding now is that transverse wave can reflect only because spring like attraction between each sphere/atom. Continuing sphere/spring metaphor. Last sphere is in resting state and connected to wall. Wave comes pulls the sphere up which causes spring to stretch up and spring compresses back which pulls sphere down and new wave starts, follow? – Muhammad Umer Feb 21 '19 at 10:35

A destructive interference does not imply that the two waves are "destroyed", it means that the sum of both waves at that point is equal to zero.

You should treat the waves as if they were two functions. Using this analogy, let us take $$f_1(x)=x$$ and $$f_2(x)=-x$$ (they are clearly not waves, they don't have a time dependence, but this will simplify the example). The addition of both functions is equal to zero at $$x=0$$, but that doesn't mean that the sum of those two functions sould be zero everywhere beyond the destructive interference.

• i was looking to understand how momentum gets transferred on small scale as such it doesn't cancel out. Not how to describe momentum mathematically. – Muhammad Umer Feb 21 '19 at 7:51
• Momentum does get transferred even when the sphere doesn't move. The key is that the same amount of momentum is being transferred to both sides of the sphere. – TheAverageHijano Feb 21 '19 at 7:56