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  • A standing wave is formed by two harmonic waver <img alt="\mathrm{y_1=A \sin (k x-\omega t) }" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7By_1%3DA%20%5Csin%20%28k%20x-%5Comega%

A standing wave is formed by two harmonic waver \mathrm{y_1=A \sin (k x-\omega t) } and \mathrm{y_2=A(k x+\omega t)} travelling on a string in opposite directions. Mass density of the string is \rho  and area of cross section is s. The total mechanical energy between two adjacent nodes on the string. is

Option: 1

\mathrm{\frac{\rho A^2 \omega^2 \pi s}{k} }


Option: 2

\mathrm{\frac{\rho A^2 \omega^2 \pi s}{2 k}}


Option: 3

\mathrm{ - \frac{\rho A^2 \omega \pi s}{k} }


Option: 4

None


Answers (1)

best_answer

The distance between two adjacent nodes is \mathrm{\frac{\lambda}{2} or \frac{\pi}{k} } 

\therefore volume of string between two nodes willablev= (area of cross section) (distance between two nodes)

\mathrm{=s \cdot \frac{\pi}{k}}
Energy density \mathrm{U=\frac{1}{2} \rho A^2 \omega^2}

then
\mathrm{E}=2 [energy stored in a distance of \mathrm{\frac{\pi}{k}} of a travelling wave]
E=2 (energy storedensity) (volume)
\begin{aligned} & \mathrm{E=2 \left (\frac{1}{2} \rho A^2 \omega \right ) S \cdot \frac{\pi}{k}} \\ & \mathrm{E=\frac{\rho A^2 \omega^2 \pi s}{L}} \end{aligned}

 

Posted by

Ajit Kumar Dubey

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