Question

The amplitude of a wave represented by displacement equation $y=\frac{1}{\sqrt{a}}sin\omega t\pm \frac{1}{\sqrt{b}}cos\omega t$ will be

• A. $\frac{a+b}{ab}$
• B. $\frac{\sqrt{a}+\sqrt{b}}{ab}$
• C. $\frac{\sqrt{a}\pm \sqrt{b}}{ab}$
• D. $\sqrt{\frac{a+b}{ab}}$

Answer 1

The correct option is D

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

$Assume\frac{1}{\sqrt{a}}=Acos\theta$ (i)

$\frac{1}{\sqrt{b}}=Asin\theta$ (ii)

On simplifying, we get $y=Asin(\omega t\pm \theta )$

Squaring and adding Eqs. (i) and (ii) $A=\sqrt{\frac{a+b}{ab}}$