Question

The transverse displacement of a string (clamped at its both ends) is given by $y(x,t)=0.66\sin (2\pi x/3)\cos (120\pi t)$ All the points on the string between two consecutive nodes vibrate with

• A. same frequency
• B. same phase
• C. same energy
• D. different amplitude

Answer 1

Answer: (A), (B), (D)

The given equation is $y(x,t)=0.06\sin \left(\frac{2\pi x}{3}\right)\cos (120\pi t)$
It represents a stationary wave.
Therefore, all the points between two consecutive nodes.
(a) vibrate with same frequency
(b) in same phase, but
(d) different amplitudes. The amplitude is zero at nodes and maximum at antinodes (between the nodes).