Equation of a standing wave is generally expressed as
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Say we have 2 equations of progressive wave as y1=Asin(kx+ωt) and y2=Asin(kx-ωt)
✔Where ω=kv, k=Wave Number, v=Wave velocity These equations combine according to the principle of superposition as:
⭐ y1+y2=[2Asin(kx)]cos(ωt). Now we know that a standing wave is called so because all the points on the wave are not translating, they are just oscillating about their mean position with different amplitudes. But if we look in the wave equation, we see that there is a cos(ωt) factor in the equation of a standing wave and since ω=kv, we can say that a standing wave has a velocity dependence also
✔Where ω=kv, k=Wave Number, v=Wave velocity These equations combine according to the principle of superposition as:
⭐ y1+y2=[2Asin(kx)]cos(ωt). Now we know that a standing wave is called so because all the points on the wave are not translating, they are just oscillating about their mean position with different amplitudes. But if we look in the wave equation, we see that there is a cos(ωt) factor in the equation of a standing wave and since ω=kv, we can say that a standing wave has a velocity dependence also
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Say we have 2 equations of progressive wave as y1=Asin(kx+ωt) and y2=Asin(kx-ωt)
✔Where ω=kv, k=Wave Number, v=Wave velocity These equations combine according to the principle of superposition as:
⭐ y1+y2=[2Asin(kx)]cos(ωt). Now we know that a standing wave is called so because all the points on the wave are not translating, they are just oscillating about their mean position with different amplitudes. But if we look in the wave equation, we see that there is a cos(ωt) factor in the equation of a standing wave and since ω=kv, we can say that a standing wave has a velocity dependence also
Explanation:
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