Question

A stationary wave is expressed as $ y=4\sin \left( \frac{\pi x}{3} \right)\cos (40\pi t) $ where $ x $ and y are measured in cm and time t in second. The separation between consecutive nodes is

• A. 1.5 cm
• B. 6 cm
• C. 12 cm
• D. 3 cm

Answer 1

Answer: (D)

: $ y=4\sin \left( \frac{\pi x}{3} \right)\cos (4\pi t) $ Standard equation of a stationany wave is $ y=2a\sin \left( \frac{2\pi x}{\lambda } \right)\cos \left( \frac{2\pi vt}{\lambda } \right) $ $ \therefore $ $ \frac{2\pi x}{\lambda }=\frac{\pi x}{3} $ or $ \lambda =6\,cm $ Distance between consecutive nodes $ =\lambda /2 $ $ =6/2=3\text{ }cm $