Question

The transverse displacement of a string clamped at its both ends in given by
$y(x,T)=2sin\left(\frac{2\pi }{3}x\right)cos\left(100\pi t\right)$ Where $x$ and $y$ are in cm and $t$ is in $s$. Which of the following statement 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, 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.

Answer 1

The correct option is B All the points on the string between two consecutive nodes vibrate with same frequency, phase but different amplitude.

The given equation is
$y(x,t)=2sin\left(\frac{2\pi }{3}x\right)cos\left(100\pi t\right)$
It represents a stationary wave. Therefore, all the points between consecutive nodes vibrate with same frequency and same but different amplitude.