JEE Class main Answered

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

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

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

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

Hence , we get ,

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)

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   cm/s  and particle speed = -2π cm/s