MCQ
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

  • $\frac{{\sqrt {a + b} }}{{\sqrt {ab} }}$
  • B
    $\frac{{\sqrt a  + \sqrt b }}{{ab}}$
  • C
    $\frac{{\sqrt a  - \sqrt b }}{{ab}}$
  • D
    $\frac{{\sqrt {a - b} }}{{\sqrt {ab} }}$

Answer

Correct option: A.
$\frac{{\sqrt {a + b} }}{{\sqrt {ab} }}$
a
Ideal equation

$y=\sqrt{\left(\frac{1}{\sqrt{a}}\right)^{2}+\left(\frac{1}{\sqrt{b}}\right) \sin (\omega t+\phi)}$

$\mathrm{y}=\left(\frac{1}{\mathrm{a}}+\frac{1}{\mathrm{b}}\right) \sin (\omega \mathrm{t}+\phi)$

amplitude $A=\sqrt{\frac{1}{a}+\frac{1}{b}}=\sqrt{\frac{a+b}{a b}}$

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