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Q.
For the stationary wave $y=4 \sin \left(\frac{\pi x}{15}\right) \cos (96 \pi t)$, the distance between a node and the next antinode is
Waves
Solution:
Comparing given equation with standard equation
$y=2 a \sin \frac{2 \pi x}{\lambda} \cos \frac{2 \pi v t}{\lambda}$ gives us
$\frac{2 \pi}{\lambda}=\frac{\pi}{15}$
$\Rightarrow \lambda=30$
Distance between nearest node and antinodes
$=\frac{\lambda}{4}=\frac{30}{4}=7.5$