Question 400: Waves

Question

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 $$\left(\cos 90^{\circ}=0\right)$$

Accepted Answer

$$y=\frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \sin \left(\omega t+\frac{\pi}{2}\right)$$
Here phase difference $$=\frac{\pi}{2}$$
The resultant amplitude
$$=\sqrt{\left(\frac{1}{\sqrt{a}}\right)^2+\left(\frac{1}{\sqrt{b}}\right)^2}=\sqrt{\frac{1}{a}+\frac{1}{b}}=\sqrt{\frac{a+b}{a b}}$$

Answer

$$\frac{a \pm b}{a b}$$

Answer

$$\frac{\sqrt{\mathrm{a}} \pm \sqrt{\mathrm{b}}}{\mathrm{ab}}$$

Answer

$$\frac{\sqrt{\mathrm{a}} \pm \sqrt{\mathrm{b}}}{\sqrt{\mathrm{ab}}}$$

Answer

$$\sqrt{\frac{a+b}{a b}}$$

Waves

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)

Choose the correct answer: