Question

Two waves of intensities $I$ and $4I$ superimpose. The minimum and maximum intensities will respectively be

• A. $I,9I$
• B. $3I,5I$
• C. $I,5I$
• D. None of these

Answer 1

The correct option is A $I,9I$

The Intensity of the wave is directly proportional to the square of its amplitude.

$I\propto A^2$;

$I=cA$${}^2$; '$c$' is an arbitrary constant.

So, if a wave with Intensity $I$ has an amplitude of $A(A{}_1$)

A wave with an Intensity of $4I$ would respectively have an amplitude of $2A$($A{}_2$)

If 2 waves with amplitudes $A{}_1$,$A{}_2$ are superimposed, the resultants would be

Maximum of $A{}_1$ + $A{}_2=3A$ (Constructive Interference)

Minimum of $|A{}_1$ - $A{}_2|=A$ (Destructive Interference)

The wave of amplitude $3A$ would have an Intensity of $9I$

The wave of amplitude $A$ would have an Intensity of $I$