Question

The equation of a stationary wave is $y=4\sin \frac{\pi x}{5}\cos \left(100\pi t\right)$. The wave is formed using a string of length $20cm$. The second and 3rd antinodes are located at positions (in cm)

• A. $7.5,12.5$
• B. $2.5,7.5$
• C. $12.5,17.5$
• D. $5,10$

Answer 1

Answer: (A)

$7.5,12.5$

$y=4\sin \frac{\pi x}{5}\cos 100\pi t$

For antinodes

$\sin \frac{\pi x}{5}=1\Rightarrow \frac{\pi x}{5}=(2n+1)\frac{\pi }{2}\Rightarrow x=(2n+1)\frac{5}{2}\Rightarrow n=0,x=\frac{5}{2}=2.5\Rightarrow n=1,x=\frac{15}{2}=7.5\Rightarrow n=2,x=\frac{25}{2}=12.5$

For second and third antinodes will be at

$x=7.5,x=12.5$

Correct option is A