Equations of a stationary and a travelling waves are as follows $$y1$$ $$=$$ a $$sin$$ $$kx$$ $$cos$$ ωt and $$y2$$ $$=$$ a $$sin$$ ωt $$-$$ Kx The phase difference between two points $$x1$$ $$=$$ π$$3k$$ and $$x2$$ $$=$$ $$3$$$$π$$$$3k$$ are ϕ$$1$$ and ϕ$$2$$ respectively for the two waves. The ratio ϕ$$1$$ϕ$$2$$ is

Question

Equations of a stationary and a travelling waves are as follows $$y1$$ $$=$$ a $$sin$$ $$kx$$ $$cos$$ ωt and $$y2$$ $$=$$ a $$sin$$ ωt $$-$$ Kx The phase difference between two points $$x1$$ $$=$$ π$$3k$$ and $$x2$$ $$=$$ $$3$$$$π$$$$3k$$ are ϕ$$1$$ and ϕ$$2$$ respectively for the two waves. The ratio ϕ$$1$$ϕ$$2$$ is

Infinity Learn · Accepted Answer

At $$x1$$ $$=$$ π$$3k$$ and $$x2$$ $$=$$ $$3$$$$π$$$$2k$$ $$sin$$ $$Kx1$$ or $$sin$$ $$Kx2$$ is not zero. Therefore, neither of $$x1$$ or $$x2$$ is a node Δx $$=$$ $$x2$$ $$-$$ $$x1$$ $$=$$ $$32$$ $$-$$ $$13$$$$π$$k $$=$$ $$7$$$$π$$$$6k$$ Since $$2$$$$π$$k  > Δx > πk λ > Δx > λ$$2$$   k $$=$$ $$2$$πλ Therefore, ϕ$$1$$ $$=$$ π and ϕ$$2$$ $$=$$ k Δx $$=$$ $$7$$$$π$$$$6$$ ∴ ϕ$$1$$ϕ$$2$$ $$=$$ $$67Note$$ : In case of stationary wave phase difference between any two points is either zero of π .

Equations of a stationary and a travelling waves are as follows y1 = a sin kx cos ωt and y2 = a sin ωt - Kx The phase difference between two points x1 = π3k and x2 = 3π3k are ϕ1 and ϕ2 respectively for the two waves. The ratio ϕ1ϕ2 is

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