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  4. The superposition takes place between two waves of frequency f and amplitude a . The maximum intensity Imax=constant ×

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Q. The superposition takes place between two waves of frequency $f$ and amplitude $a$ . The maximum intensity $I_{max}=constant \times$ ____

NTA AbhyasNTA Abhyas 2020Waves

Solution:

Resultant amplitude
$A=\sqrt{a^{2} + a^{2} + 2 a a cos \phi}=\sqrt{4 a^{2} \left(cos\right)^{2} ⁡ \left(\frac{\phi}{2}\right)}$
$A=2acos \left(\frac{\phi}{2}\right)$
$\therefore \, \, \, I \propto A^{2}$
$\Rightarrow \, \, \, I \propto 4a^{2}$