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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$\frac{π}{5}$

$π$

2 $π$ /5

answer is B.

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Detailed Solution

for nodes, $\sin \frac{πx}{15} = 0$
$\frac{πx}{15} = 0, π, 2 π, 3 π, . .........$
x=0,15,30,45,……
No. of nodes between 13cm to 16cm
is “1 at 15cm”.
Phase difference $ϕ = nπ = π$

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