Three waves of equal frequencies having amplitudes $10\ \mu ext{m}$, $4\ \mu ext{m}$ and $7\ \mu ext{m}$ arrive at a given point with successive phase difference of $\frac{\pi}{2}$. The amplitude of the resulting wave (in $\mu ext{m}$) is given by

Question

Three waves of equal frequencies having amplitudes $10\ \mu	ext{m}$, $4\ \mu	ext{m}$ and $7\ \mu	ext{m}$ arrive at a given point with successive phase difference of $\frac{\pi}{2}$. The amplitude of the resulting wave (in $\mu	ext{m}$) is given by

Aicharya · Accepted Answer

Using vector algebra, [The diagram shows two opposite horizontal vectors of $10\ \mu	ext{m}$ and $7\ \mu	ext{m}$ resolving into a net horizontal vector of $3\ \mu	ext{m}$, perpendicular to a vertical vector of $4\ \mu	ext{m}$.] $\Rightarrow$ Resulting wave, $A_R = \sqrt{(4)^2 + (3)^2} = 5\ \mu	ext{m}$

Three waves of equal frequencies having amplitudes $10\ \mu\text{m}$, $4\ \mu\text{m}$ and $7\ \mu\text{m}$…

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