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The transverse displacement of a string ...

The transverse displacement of a string (clamped at its both ends ) is given by `y(x,t)=0.06sin(2pix//3)cos(120pit).`
All the points on the string between two consecutive nodes vibrate with

A

same frequeny

B

same phase

C

same enrgy

D

different amplitude

Text Solution

Verified by Experts

The correct Answer is:
A, D
Given equation is `" " y(x,t)=0.06 sin ((2pix)/(3)) cos (120pit)`
Comparing with standard equation of stationary wave
`" " y(x,t)=a sin (kx) cos (omegat)`
It is represented by diagram.
Where N donotes nodes and A denotes antinodes.

(a) Clearly, frequency is common for all the points.
(b) Consider all the patiles between two they are having same phase of `(120pit)` at a given time.
(c) and (d) But are having effect amplitudes of `0.06 nsin ((2pi)/(3)x)` and because of different amplitude they are having different energies.
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