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System Of Particles And Rotational Motion

Question

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The equation of stationary wave along a stretched string is given by $y = 5 \sin \frac{πx}{3} \cos 40 πt$ where, x and y are in cm and t in second. The separation between two adjacent nodes is :

1.5 cm

3 cm

6 cm

4 cm

Solution

B.

3 cm

Given equation

$y = 5 \sin \frac{πx}{3} \cos 40 πt$

Compairing with standard equation

y = A sin kx cosωt

$∴ k = π / 3 \Rightarrow \frac{2 π}{3} = \frac{π}{3} λ = 6 cm Separation between two cosecutive nodes \frac{λ}{2} = \frac{6}{2} = 3 cm$

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