We know that at least the waves inside a flute or laser make resonance waves,and simply we know that a standing wave is superposition of two waves that are propagating in oposit direction,for example Asin(kx-wt)+Asin(kx+wt)=2Asi(kx)cos(wt).which the result is telling you that the wave is not prapagating to any direction.i belive that these standing waves are not wave,becouse they are neither transverse nor longitudinal and they have no prpagation in any direction.another reason is that they are not satisfying in a general formulation of wave,it means f(x-vt).i want to understand is my conclusion right or not? And secondly if they are not propagating how we see the beam of laser,or how we hear the resonance of a flute? Are the waves that coming out of the cavity of laser or cavity of a flute standing waves? Or just inside them we have standing wave? if the outside wave of cavity is standing waves ,they are superposition of what two oposit propagating wave?and if no, the wave of outside cavity not a standing wave ,how is it possible that we hear the resonance of a flute even out of a cavity?
closed as unclear what you're asking by CuriousOne, ACuriousMind♦, Gert, user36790, John Rennie Feb 3 '16 at 8:27
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The problem in answering this question is that the term wave itself is so loosely used to define that which we observe.
But fundamentally a wave is just an expression of the flow of energy in time and space. It's observable evidence that energy is flowing. It's clear that traveling waves expresses the flow of energy. And the interference or superposition of two or more traveling waves can create this wave-like thing we observe and call a standing wave. The standing wave looks like a wave and is indeed caused by energy flow, so why not call it it a wave? Can you think of a better name that might more clearly define it?
$f(x-vt)$ isn't the general formulation of a wave, but is the general expression for a travelling wave. Also, a standing wave can be transverse or longitudinal (on a guitar string or inside a laser cavity it is transverse, inside a flute it is longitudinal).
The reason you can hear the sound of a flute is because some of the energy coming from the standing wave radiates outside of the cavity in the form of travelling spherical waves.