The transverse displacement of a string clamped at its both ends is given by $y(x, t) = 2 \sin \left( \frac{2\pi}{3} x \right) \cos (100 \pi t)$,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 two consecutive nodes vibrate with different frequency,phase and amplitude.