The transverse displacement of a string (clamped at its both ends… - Vidyadip

MCQ

The transverse displacement of a string $($clamped at its both ends$)$ is given by $\text{y}(\text{x, t})=0.06\sin(1\pi\text{x/ 3})\cos(120\pi\text{t}).$
All the points on the string between two consecutive nodes vibrate with

A
Same frequency.
B
Same phase.
C
Different amplitude.
✓
All of the above

✓

Answer

Correct option: D.

All of the above

The frequencies of all particles are same, verifies the option $(a).$
particles between any two consecutive nodes vibrates either upside or downside having sameb phase $120\pi\text{t}$ any time, verifies the option $(b)$
particles have ditternt energies. so rejects the option $(c)$
As the amplitude of different particles are diffrent between two nodes energy $(E) \propto\text{A}^2.$

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