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 $4\, m .$
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 $y=2 a \sin k x \cos \omega t$
$k=\frac{\pi}{4}$
As $\lambda=\frac{2 \pi}{k}$
$\therefore \lambda=\frac{2 \pi}{\pi / 4}=8\, m$
Distance between two consecutive antinodes
$=\frac{\lambda}{2}=\frac{8}{2}=4\, m$