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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 (600pit)`
Comparing with
`Y= 2 A sin ((2pix)/lambda)cos ((2pit)/T)`
we get, `(2pix)/lambda=0.314x`
`therefore lambda = (2xx3.14)/(0.314)= 20` cm
`therefore` Length of one loop `=lambda/2 = 10` cm
There are 3 loops for the third harmonic.
`therefore` Length = 30 cm
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-STATIONARY WAVES -EXERCISE 1
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