Two identical sinusoidal waves each of amplitude $10 \mathrm{~mm}$, with a phase difference of $90^{\circ}$…
Two identical sinusoidal waves each of amplitude $10 \mathrm{~mm}$, with a phase difference of $90^{\circ}$ are travelling with the same direction in a string. The amplitude of the resultant wave is
$5 \mathrm{~mm}$
$10 \sqrt{2} \mathrm{~mm}$
$5 \sqrt{2} \mathrm{~mm}$
$20 \mathrm{~mm}$
Solution
Given that, amplitudes of two waves are
$a_1=a_2=10 \mathrm{~mm}$
Phase difference, $\phi=90^{\circ}$
Let $A$ be the resultant amplitude, then by using expression,
$A=\sqrt{a_1^2+a_2^2+2 a_1 a_2 \cos \phi}$
Substituting the values, we get
$\begin{aligned} A & =\sqrt{(10)^2+(10)^2+2(10)(10) \times \cos 90^{\circ}} \\ & =10 \sqrt{2} \mathrm{~mm}\end{aligned}$