Question

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

(correct answer + 2, wrong answer - 0.50)

• A. $7.5\text{units}$
• B. $1.5\text{units}$
• C. $22.5\text{units}$
• D. $30\text{units}$

Answer 1

The correct option is A $7.5\text{units}$

$y=4\sin \left(\frac{\pi x}{15}\right)\cos \left(96\pi t\right)$ ... (1)
General equation of stationary wave
$y=2a\sin kx\cos \omega t$ ... (2)
from comparison 1 & 2
$k=\frac{\pi }{15}=\frac{2\pi }{\lambda }$
$\Rightarrow \lambda =50$
Distance between nearest node and
Antinode $=\lambda /4=\frac{30}{4}=7.5\text{unit}$