Question

The equation of a stationary wave is
y = 4 sin $\left(\frac{\pi x}{5}\right)$ cos $\left(100\pi t\right)$.

The wave is formed using a string of length 20cm. The second and 3rd antinodes are located at position ( in cm )

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

Answer 1

The correct option is D 5, 10

Given,

$y=4\sin \left(\frac{\pi x}{5}\right)\cos \left(100\pi t\right)$

Standing wave equation $y=4\sin \left(kx\right)\cos \left(\omega t\right)$

On compare both, $k=\frac{2\pi }{\lambda }=\frac{\pi }{5}$

$\lambda =10cm.$

Nodes at $\frac{n\lambda }{2}(0,1,2...)$

Second node $(n=1)$, $\frac{\lambda }{2}=\frac{10}{2}=5cm$

Third node $(n=2)$, $\frac{2\lambda }{2}=\frac{2\times 10}{2}=10cm$