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

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

Hint:

Logic Tip: Orthogonal wave components (sine and cosine) combine using the Pythagorean theorem for the resultant amplitude.

Answer 1

The Correct Option is D