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JEE Class main Answered

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Asked by piyurawriya | 20 Feb, 2024, 01:03: PM
answered-by-expert Expert Answer

From the displacement-time (y-t) graph , we get period of wave T = 2 s .

Hence frequency f = 1/T = 1/2 s-1 = 0.5 s-1

From the displacement-position (y-x) graph , we get wavelength of wave λ = 2 cm .

Wave velocity = f λ = 0.5 × 2  cm/s = 1 cm/s

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From displacement-time (y-t) graph , we get displacement as a function of time is

img ....................... (1)

where A = 4 cm is amplitude of wave and ω  is angular frequency .

img

if the displacement y = 2√3 cm , then from eqn.(1) , we get

img

Hence , we get ,

img

since the displacement is when the amplitude is decreasing , we have

π t = (2 π ) / 3  or   t = ( 2/3 ) s

velocity of particle is calculated by differentiating eqn.(1)

img

v(t) = 4 × π × cos( π × (2/3) ) = - 2π

Since wave propagation direction is along x-axis and velocity of particle is along y axis,

Wave  speed = 1 img  cm/s  and particle speed = -2π img cm/s

Answered by Thiyagarajan K | 20 Feb, 2024, 06:34: PM
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