1. Tardigrade
  2. Question
  3. Physics
  4. 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:

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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:

Waves

Solution:

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