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 $\lambda =6cm$ Distance between consecutive nodes $=\lambda /2$ $=6/2=3cm$