Question

A sinusoidal progressive wave is generated in a string. It's equation is given by $y=\left(2mm\right)\sin (2\pi x-100\pi t+\pi /3).$ The time when particle at $x=4m$ first passes through mean position, will be

• A. $\frac{1}{150}sec$
• B. $\frac{1}{12}sec$
• C. $\frac{1}{300}sec$
• D. $\frac{1}{100}sec$

Answer 1

Answer: (C)

$\frac{1}{300}sec$

Given the wave's equation:
$y=\left(2mm\right)\sin (2\pi x-100\pi t+\frac{\pi }{3})$; we substitute $x=4$;
The equation simplifies to:
$y=\left(2mm\right)\sin (8\pi -100\pi t+\frac{\pi }{3})$;

but $\sin (2n\pi +a)$ = $\sin \left(a\right)$

and the equation further simplifies to
$y=\left(2mm\right)\sin (-100\pi t+\frac{\pi }{3})$;
For mean position the argument within the sine should be zero.
$-100\pi t+\frac{\pi }{3}=0$;
or, $t=\frac{1}{300}$s