Question

Assertion The equation of a stationary wave is $y=20\sin \frac{\pi x}{4}\cos \omega t$ The distance between two consecutive anti-nodes will be $4m.$
Reason The data is insufficient.

• A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion
• B. If both Assertion and Reason are true but. Reason is not correct explanation of the Assertion
• C. If Assertion is true butt Reason is false
• D. If Assertion is false but the Reason is true

Answer 1

Answer: (C)

The equation of stationary waves is
$y=20\sin \frac{\pi x}{4}\cos \omega t$
Compare with $y=2a\sin kx\cos \omega t$
$k=\frac{\pi }{4}$
As $\lambda =\frac{2\pi }{k}$
$\therefore \lambda =\frac{2\pi }{\pi /4}=8m$
Distance between two consecutive antinodes
$=\frac{\lambda }{2}=\frac{8}{2}=4m$