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Question

A transverse wave on a string has an amplitude of 0.2 m and a frequency of 175 Hz. Consider a particle of the string at x = 0. It begins with a displacement y = 0, at t = 0, according to equation y=0.2 sin (kx±ωt). How much time passes between the first two instant when this particle has a displacement of y = 0.1 m?

A
1.9 ms
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B
3.9 ms
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C
2.4 ms
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D
0.5 ms
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Solution

The correct option is A 1.9 ms
y=(0.2 m) sin[kx±ωt]For x=0, y=0.1 m0.1=0.2 sin (ωt)ωt=π6 or 5π6So, t2=5π6ω and t1=π6ωt2t1=2π3ω=13f=1.9 ms

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