Question

Assertion :Two waves $y_1$ = A sin $(\omega t+kx)$ and $y_1$ = A cos $(\omega t-kx)$ are superimposed, then x = o, becomes a node. Reason: At node net displacement due to two waves should be zero.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

Upon superimposing the waves and putting x= 0;
We get:
$y=Asin\omega t+Acos\omega t$
$y=\sqrt{2}Asin(\omega t+\frac{\pi }{4})$
As we can see displacement of this particle is zero only at select time intervals, it doesn't qualify to be a node.
A node is a point of zero permanent displacement.
Hence assertion is incorrect, reason is correct.