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Q.

The vibrations of a string fixed at both ends are represented by $large y, = ,16sin frac{{pi x}}{{15}}cos 96pi t$ 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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a

$\frac{π}{5}$

b

$π$

c

zero

d

$\frac{2 π}{5}$

answer is B.

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Detailed Solution

large k, = ,frac{{2pi }}{lambda } = ,frac{pi }{{15}},,,therefore ,lambda , = ,30cm

The distance between two successive nodes is

large frac{lambda }{2}, = ,15cm

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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The vibrations of a string fixed at both ends are represented by 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