Two waves having amplitudes in the ratio 5:1 produce interference. The ratio of the maximum to minimum…
Two waves having amplitudes in the ratio 5:1 produce interference. The ratio of the maximum to minimum intensity is
$6: 4$
$25: 1$
$3: 2$
$9: 4$
Solution
Let the amplitudes be $5 x$ and $x$ respectively.
The resultant waves will have maximum amplitude when both are in phase
Therefore, amplitudes should add up to $5 x+x=6 x$
During destructive interference, the waves are out of phase
Therefore, the resultant amplitude is $x-5 x=-4 x$
Maximum intensity $\propto(\text { maximum amplitude })^2=36 x^2$
Minimum intensity $\propto(\text { minimum amplitude })^2=16 x^2$
The ratio of the maximum to minimum intensity $=\frac{36}{16}=\frac{9}{4}$