Question

A wave pulse is traveling on a string at 2 m/s. Displacement y of the particle at x = 0 at any time t is given by $\frac{2}{(t^2+1)}$. Find the expression of the function y = (x, t), i.e., displacement of the particle at position x and time t.

• A. $y=\frac{2}{{(t-\frac{x}{2})}^2+1}$
• B. $y=\frac{2}{{(t-\frac{x}{4})}^2+1}$
• C. $y=\frac{2}{{(t-2x)}^2+1}$
• D. $y=\frac{2}{{(t-4x)}^2+1}$

Answer 1

The correct option is A $y=\frac{2}{{(t-\frac{x}{2})}^2+1}$

Replacing $t\to t-\frac{x}{v}=t-\frac{x}{2}$, we get $y=\frac{2}{{(t-\frac{x}{2})}^2+1}$