Question

Assertion: In the equation, $y=A\sin (kx-\omega t)$ , particle starts from its mean position $x=0$ and moves towards negative $y-$axis.
Reason: The wave corresponding to given equation is travelling towards positive $x-$direction.

• A. Both assertion and reason are correct and reason is the correct explanation of assertion.
• B. Both assertion and reason are correct but reason is not a correct explanation of assertion.
• C. Assertion is correct but reason is incorrect.
• D. Assertion is incorrect but reason is correct.

Answer 1

The correct option is B Both assertion and reason are correct but reason is not a correct explanation of assertion.

Given, $y=A\sin (kx-\omega t)$
At $x=0$,
$\Rightarrow y=-A\sin \omega t$
further putting $t=0$ gives $y=0$. This means wave motion starts from mean position towards negative $y-$axis.
$\Rightarrow$ Assertion is correct.
The phase value $(kx-\omega t)$ signifies that the wave is moving towards $+ve,x-$axis.
$\Rightarrow$ Reason is correct.
But, reason is not correct explanation of assertion.
$\therefore$ Option $\left(b\right)$ is correct.