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  4. Displacement - time graphs for two waves, wave - 1 and wave - 2 are shown here. The ratio of the intensity of wave - 1 to that of wave - 2 is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-r0otjbjwztgk.png />

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Q. Displacement - time graphs for two waves, wave - $1$ and wave - $2$ are shown here. The ratio of the intensity of wave - $1$ to that of wave - $2$ is

Question

NTA AbhyasNTA Abhyas 2020Waves

Solution:

Average intensity along the string
$ < I> \, =2\pi ^{2}f^{2}A^{2}ϱv$
$\frac{l_{1}}{l_{2}}=\left(\frac{f_{1} A_{1}}{f_{2} A_{2}}\right)^{2}=\left(\frac{T_{2} A_{1}}{T_{1} A_{2}}\right)^{2}=\left(\frac{1}{2} \times 3\right)^{2}=\frac{9}{4} \, $