At t=0, a transverse wave pulse travelling in the positive x direction with a speed of 2 m / s in a wire is described by the function y=(6/x2), given that x ≠ 0 . Transverse velocity of a particle at x=2 m and t=2 seconds is:

Question

At t=0, a transverse wave pulse travelling in the positive x direction with a speed of 2 m / s in a wire is described by the function y=(6/x2), given that x ≠ 0 . Transverse velocity of a particle at x=2 m and t=2 seconds is: (A) 3 m/s (B) -3 m/s (C) 8 m/s (D) -8 m/s

Tardigrade Admin · Accepted Answer

y(x, t=0)=(6/x2) then y(x, t)=(6/(x-2 t)2) ⇒ ( partial y/ partial t)=(24/(x-2 t)3) at x=2, t=2 Vy=(24/(-2)3)=-3 m / s

Q. At $t = 0$ , a transverse wave pulse travelling in the positive $x$ direction with a speed of $2 m / s$ in a wire is described by the function $y = \frac{6}{x ^{2}}$ , given that $x \neq = 0.$ Transverse velocity of a particle at $x = 2 m$ and $t = 2$ seconds is:

3 m/s

-3 m/s

8 m/s

-8 m/s

$y (x, t = 0) = \frac{6}{x ^{2}}$ then $y (x, t) = \frac{6}{( x - 2 t ) ^{2}}$
$\Rightarrow \frac{\partial y}{\partial t} = \frac{24}{( x - 2 t ) ^{3}}$
at $x = 2, t = 2$
$V_{y} = \frac{24}{( - 2 ) ^{3}} = - 3 m / s$

Q. At t=0, a transverse wave pulse travelling in the positive x direction with a speed of 2m/s in a wire is described by the function y=x26​, given that x=0. Transverse velocity of a particle at x=2m and t=2 seconds is: