Question

The equation of stationary wave is $y=4\text{sin}\left(\frac{\pi x}{15}\right)\text{cos}\left(96\pi t\right)$. The distance between a node and its next antinode is

• A. 7.5 units
• B. 1.5 units
• C. 22.5 units
• D. 30 units

Answer 1

The correct option is A

7.5 units

$y=4\text{sin}\left(\frac{\pi x}{15}\right)\text{cos}\left(96\pi t\right)$ ....(1)

$y=2a\text{sin kx cos}\omega t$ ...... (2)

from comparison 1 and 2

$k=\frac{\pi }{15}=\frac{2\pi }{\lambda }$

$\lambda =30$

Distance b/w nearest node and Antinode $=\frac{\lambda }{4}$

$=\frac{30}{4}=7.5\text{unit}$