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Question

The vibrations of a string of length 60 cm fixed at both ends are represented by the equation y=4 sin(πx15)cos(96πt) where x and y are in centimeters and t is in seconds. The maximum displacement of a point at x=5 cm is

A
23cm
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B
2cm
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C
43cm
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D
None of the above
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Solution

The correct option is A 23cm
y=4sin(πx15)cos(96πt)
The maximum displacement will be when cos(96πt)=1
ymax=4sin(πx15)
ymax at x=5cm
=4sin(π×515)
=4×sin(π3)
=4×32=23cm

959952_969650_ans_aca84eaa16b14b769167c0e7517aaf04.PNG

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