The transverse displacement of a string clamp | vedclass

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(B) The given equation is $y(x, t) = 2 \sin \left( \frac{2 \pi}{3} x \right) \cos (100 \pi t)$.This equation represents a standing (stationary) wave.I

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) The given equation is $y(x, t) = 2 \sin \left( \frac{2 \pi}{3} x \right) \cos (100 \pi t)$.This equation represents a standing (stationary) wave.In a standing wave,all particles between two consecutive nodes oscillate with the same frequency $(f = 50 \ Hz)$ and are in the same phase (they reach their extreme positions simultaneously).However,the amplitude of vibration depends on the position $x$,given by $A(x) = |2 \sin (\frac{2\pi}{3} x)|$.Since $x$ varies between two consecutive nodes,the amplitude $A(x)$ varies for each point.Therefore,all points between two consecutive nodes vibrate with the same frequency and phase but different amplitudes.

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?

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