Question

If the ratio of amplitudes of two waves at any point in the medium is $1:3$, then the ratio of maximum and minimum intensities because of their superposition will be

• A. $2:1$
• B. $3:1$
• C. $4:1$
• D. $2:3$

Answer 1

The correct option is C $4:1$

Ratio of amplitudes of the two waves is $\frac{A_1}{A_2}=\frac{1}{3}$.
The maximum intensity of the superimposed waves is
$I_{max}=(A_1+A_2{)}^2=16A_1^2$.
The minimum intensity of the superimposed waves is
$I_{min}=(A_1-A_2{)}^2=4A_1^2$.
The ratio of the max and min intensity is
$\frac{I_{max}}{I_{min}}=\frac{16}{4}=\frac{4}{1}$.
Ans: C