Equation of simple harmonic progressive wave is given by $y=\frac{1}{\sqrt{a}} \sin \omega t \pm…
Equation of simple harmonic progressive wave is given by $y=\frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \cos \omega t$ then the resultant amplitude of the wave is $\left(\cos 90^{\circ}=0\right)$
$\frac{a \pm b}{a b}$
$\frac{\sqrt{a} \pm \sqrt{b}}{a b}$
$\frac{\sqrt{a} \pm \sqrt{b}}{\sqrt{a b}}$
$\sqrt{\frac{a+b}{a b}}$
Solution
$y=\frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \sin \left(\omega t+\frac{\pi}{2}\right)$
Here phase difference $=\frac{\pi}{2}$
The resultant amplitude
$=\sqrt{\left(\frac{1}{\sqrt{a}}\right)^2+\left(\frac{1}{\sqrt{b}}\right)^2}=\sqrt{\frac{1}{a}+\frac{1}{b}}=\sqrt{\frac{a+b}{a b}}$