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The displacement of a string fixed at bo...

The displacement of a string fixed at both the ends is given by
`y= 0.8 sin ((pi x)/(3)) cos (60 pi t)`
where y and x in metres and t is in second. What is the wavelength and frequency of the two interfering waves ?

A

2m, 60 Hz

B

6 m 30 Hz

C

12m, 30 Hz

D

3m, 60 Hz

Text Solution

Verified by Experts

The correct Answer is:
B
` y = 0 .8 sin ((pix)/3) cos (60 pi t)` …(1)
is the equation of a standing wave.
It is produced due to interference of two simple harmonic progressive waves travelling in opposite directions along the same path. The waves are ` y_(1) = A sin ( omegat - Kx) " and " y_(2) = - A sin Kx cos ( omega t)` ...(2) Comparing (1) and (2) , we get
` K = (2pi)/lambda = pi/3 :. lambda = 6 ` metre
and ` omega = 60 pi " but " omega = 2 pi v`
` :. 2 pi v = 60 pi :. v = 60/2 = 30 ` Hz
Thus , ` lambda = 6 m " and " v = 30 ` Hz
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