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The equation of a stationary wave is y =0.8 cos $(\frac{π x}{20})$ sin 200 $π t$ where x is in cm and t is in sec . The separation between consecutive nodes will be :

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20 cm

10 cm

40 cm

30 cm

answer is A.

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Detailed Solution

Standard equation y = A cos $\frac{2 π x}{λ} \sin \frac{2 π v t}{λ}$

by comparing the equation with the given equation $\frac{2 π x}{λ} = \frac{π x}{20} \Rightarrow λ = 40 c m$

Distance between 2 nodes = $\frac{λ}{2} = 20 c m$

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