Transverse displacement of a string clamped at its both ends is given by yleft( {x,t} right) =

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14.Waves and Sound

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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 ?

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

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

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

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

Solution

The given equation is

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

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

Standard 11

Physics

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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 ?

Solution

Similar Questions

A string is stretched so that its length is increased by $\frac{1}{\eta }$ of its original length. The ratio of fundamental frequency of transverse vibration to that of fundamental frequency of longitudinal vibration will be

A steel rod $100 \,cm$ long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.53\,kHz$. What is the speed of sound in steel ….. $km/sec$

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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 ?