Question

For the stationary wave $y=4\sin \frac{\pi x}{15}\cos 96\pi t$ The distance between a node and the next antinode is

• A. 7.5cm
• B. 15cm
• C. 22.5cm
• D. 30cm

Answer 1

Answer: (A)

Given, $y=4\sin \frac{\pi x}{15}\cos 96\pi t$ For nodes, displacement is zero. $\therefore$ $\sin \frac{\pi x}{15}=0$ $\Rightarrow$ $\frac{\pi x}{15}=0,\pi ,2\pi$ $x=\frac{15}{2},\frac{45}{2}....$ For antinodes, displacement is maximum. $\therefore$ $\sin \frac{\pi x}{15}=1$ $\Rightarrow$ $\frac{\pi x}{15}=\frac{\pi }{2},\frac{3\pi }{2},....$ $x=\frac{15}{2},\frac{45}{2}....$ Hence, distance between a node and next antinode $=\frac{15}{2}-0=\frac{15}{2}=7.5cm$