Question

A wave $y=a\sin (\omega t-kx)$ on a string meets with another wave producing a node at $x=0$ . Then the equation of the unknown wave is

• A. $y=a\sin (\omega t-kx)$
• B. $y=-a\sin (\omega t-kx)$
• C. $y=a\cos (\omega t-kx)$
• D. $y=-a\cos (\omega t-kx)$

Answer 1

The correct option is B $y=-a\sin (\omega t-kx)$

$y=a\sin (\omega t-kx)$
$y_1+y_2=0atx=0$
$\therefore a\sin \omega t+y_2=0$
$y_2=-a\sin \omega t$
$\therefore y_2=-a\sin (\omega t-kx)$
$or{y}_2=-a\sin (\omega t+kx)$