Consider a hypothetical wave pulse (at time t = 0) given by the following (y, x in meter)y = 0, x &l

Question

Consider a hypothetical wave pulse (at time t = 0) given by the following (y, x in meter)

y = 0, x < 0

y = x/2, 2 > x ≥ 0

y = 3 – x, 3 ≥ x ≥ 2

y = 0, x > 3

The pulse travels leftwards (negative x direction) at speed v = 2 m/s. Which of the following plots are correct? [V_y is the velocity of particle]

Accepted Answer

Sol. y = 0 x < 0y = x/2 2 > x ≥ 0y = 3 – x 3 > x ≥ 2y = 0 x > 0$v_{y} = \frac{dy}{dt} = - v_{w}\frac{dy}{dt} = 2\frac{dy}{dx}$ [vw = – 2m/s]$v_{y} = - \frac{2dy}{dx}\left\lbrack \begin{aligned} & 0 x < 0 \ & + 1 0 \leq x < 2 \ & - 2 2 \leq x < 3 \ & 0 3 < x \end{aligned} ight.\ $

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