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The vibrations of a string fixed at both ends are represented by $y = 16 \sin \frac{πx}{15} \cos 96 πt$ where x and y are in cm and t in seconds. Then the phase difference between the points at x = 13 cm and x = 16 cm (in radian) is

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$π$

zero

$\frac{π}{5}$

$\frac{2 π}{5}$

answer is B.

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Detailed Solution

$k = \frac{2 π}{λ} = \frac{π}{15} ∴ λ = 30 cm$

The distance between two successive nodes is

$\frac{λ}{2} = 15 cm$

The two points of x = 13 cm and x = 16 cm are in adjacent loops. They vibrate in opposite phase. i.e. phase difference is $π$ radian.

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