# Is Stationary wave actually a Wave?

Okay so by the definition of a wave i.e The osciallatory disturbance in a medium which propogates energy is called as wave..the stationary wave contradicts both the crieteria as it doesnt propogate nor does it transmit any energy.

Now one may say that a stationary wave is made by two progressive waves with same phase, frequency and amplitude superimposing in opposite direction..and we know that compsition of two waves is also a new wave..by that conclusion the stationary wave must be a wave..but it contradicts the definition of a wave

So what do we call the Stationary Wave as? this was asked to me by a physics proffessor and i am pondering since.

wave

• Are you referring to the standing waves, or is this stationary wave a different “thing"? Oct 5, 2023 at 7:36
• In my view, a wave is something that satisfies a wave equation. Oct 5, 2023 at 7:55
• yup i am referring to a standing wave Oct 5, 2023 at 8:07
• Where does your definition of a wave come from? I don't think it's universal, e.g. Wikipedia uses a different definition. Oct 5, 2023 at 9:08
• >and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) is the definition cited on the wikipedia, my definition comes from a highschool physics textbook which is just a bottled down version of the definition Oct 5, 2023 at 12:31

The fact that it propagates with a velocity of zero and transfers energy at a zero rate does not preclude it being called a standing/stationary wave noting it does have energy stored in it.

What I will try and show you is that your definition of a wave is somewhat limited and needs refinement.

At this level you should perhaps use the idea that a stationary wave can be thought of a the superposition of two waves each of which satisfy the wave equation which in one dimension is, $$\dfrac{\partial^2y(x,t)}{\partial t^2} =v^2\dfrac{\partial^2y(x,t)}{\partial x^2}$$?

Doing that then introduces numerous other entities which you may not consider a wave, for example, $$y(x,t) = x-v t$$ between $$x$$ and $$x+v$$ and zero otherwise.
A wave which looks a saw tooth.

Two wave profiles are shown one at time $$t=0$$ and another at time $$t$$.

Here is a disturbance which has energy associated with it and the energy is moving in the positive x-direction.

• considering the fact that the definiton which i refer to as is a definiton cited in a highschool physics textbook..it might be the reason why the definition felt incomplete. Oct 5, 2023 at 12:34