Question

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.

Answer 1

Answer: (B)

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

Answer 2

The given equation is

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

It represents a stationary wave. Therefore, all the points between consecutive be nodes vibrate with same frequency and same phase but different amplitude.