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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 (500 $π$ t) (x, y are in cm 't' is in sec). The length of the string is

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a

24.6 cm

b

12.5 cm

c

20.6 cm

d

15.7 cm

answer is D.

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Detailed Solution

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y= 2 sin(0.6x)cos500 $π$ t
y = 2 sin kx cos $ω$ t

It is in third harmonic $\Rightarrow l = \frac{3 λ}{2} = \frac{3}{2} (\frac{2 π}{0.6})$
= 10 $π$ /2 = 5 $π$ =5 × 3.14 = 15.7 cm

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