The transverse displacement of a string clamped at its both ends is given by 

$y\left( {x,t} \right) = 2\,\sin \,\left( {\frac{{2\pi }}{3}x} \right)\,\cos \,\left( {100\,\pi t} \right)$ 

where $x$ and $y$ are in $cm$ and $t$ is in $s$. Which of the following statements is correct ?

  • A

    All the points on the string between two consecutive nodes vibrate with same frequency, phase and amplitude.

  • B

    All the points on the string between two consecutive nodes vibrate with same frequency and phase but different amplitude

  • C

    All the points on the string between two consecutive nodes vibrate with different frequency and phase but same amplitude

  • D

    All the points on the string between twoconsecutive nodes vibrate with different frequency, phase and amplitude

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