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Q.

The Equation for the vibration of a string fixed at both ends vibrating in its third harmonic is given by y = 2 sin (0.6x) cos (500πt) (x, y are in cm 't' is in sec). The length of the string is

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a

12.5 cm

b

20.6 cm

c

15.7 cm

d

24.6 cm

answer is D.

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Detailed Solution

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y=  2 sin(0.6x)cos500πt
y = 2 sin kx cosωt 

It is in third harmonic⇒l=3λ2=322π0.6
= 10π/2 = 5π =5 × 3.14 = 15.7 cm

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