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The equation of a stationary wave on a s...

The equation of a stationary wave on a string
clamped at both ends and vibrating in its third
harmonic is given by `y=0.5 sin (0.314"x") cos (600pit)`
where x and y are in cm and t is in sec. What is the
length of the string?

A

10 cm

B

20 cm

C

30 cm

D

40 cm

Text Solution

Verified by Experts

The correct Answer is:
C
`Y = 0.5 sin ( 0.314 x) cos (600 pi t)`
Comparing this with
` Y = 2A sin ((2pi x)/lambda) cos ((2 pi t)/T)`
we get , ` (2pi x)/lambda = 0.314`x
` :. lambda = (2 xx 3.14)/(0.314) = 20` cm
` :. ` Length of one loop ` = lambda/2 = 10` cm
There are 3 loops for the third harmonic .
` :. ` length = 30 cm
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