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A transverse sinusoidal wave moves along...

A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of 10 cm/s. The wavelength of the wave is 0.5 m and its ampli- tude is 10 cm. At a particular time t, the snap-shot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is Figure :

A

`(sqrt3pi)/(50)hatjm//s`

B

`-(sqrt3pi)/(50)hatjm//s`

C

`(sqrt3pi)/(50)hatim//s`

D

`-(sqrt3pi)/(50)hatim//s`

Text Solution

Verified by Experts

The correct Answer is:
A
Equation of a wave moving in tue x-axis
`y= A sin(omegat-kx) " "... (i)`
Particle velocity -
`U_p = Aomegacos(omega t-kx)" "..(ii)`
As A=10cm, y = 0.05 m = 5cm
From equation (i)
`5=10 sin(omegat – kx) = omegat-kx =pi/6`
From equation (ii)
`:. v_p=Aomega(pi/6)=0.1 xxomegaxxsqrt3/2" "..(ii)`
Now `v=lamdafimplies f =v/(lamda)=(0.10)/(0.5)=0.2`
`:. omega =2pif =2pi xx0.2 = 0.4pi`
Hence, from equation (iii)
`v_p=0.1 xx0.4 pixxsqrt3/2=sqrt3/50pi`
Direction in tue y-axis –
`v_p=sqrt3/50 pihatjm//s`
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