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Question

The equation for the vibration of a string fixed at both ends vibrating in its third harmonic is given by y=2cmsin[(0.6cm1)x]cos[500πs1(t)]. The length of the string is -

A
24.6cm
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B
31.4cm
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C
20.6cm
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D
15.6cm
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Solution

The correct option is A 15.6cm
y=2sin(0.6x)cos(500πt)
ω=500π=2πf
f=250Hz
v=ωk=500π0.6

Now,
3v2l=f

or,3×500π2×l×0.6=250

or,l=15.6 cm

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