Two wave with same frequency and wave number are propagating in the same direction. The ratio of their amplitude is $5 : 1$ . If interference occurs, the ratio of maximum and minimum intensity should be

9 : 4

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3 : 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 : 4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 : 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $9 : 4$
The ratio of maximum and minimum amplitudes corresponding to constructive and destructive interference is,
$\frac{A_{max}}{A_{min}} = \frac{A_{1} + A_{2}}{| A_{1} - A_{2} |} = \frac{A_{1} + A_{2}}{A_{1} - A_{2}}$

Given: $\frac{A_{1}}{A_{2}} = \frac{5}{1}$
Using componendo and dividendo,
$\frac{A_{1} + A_{2}}{A_{1} - A_{2}} = \frac{5 + 1}{5 - 1} = \frac{6}{4}$
$\Rightarrow \frac{A_{max}}{A_{min}} = \frac{6}{4}$
$∴ \frac{A_{max}}{A_{min}} = \frac{3}{2}$
Also intensity of wave,
$I \propto A^{2}$
$\Rightarrow \frac{I_{max}}{I_{min}} = {(\frac{A_{max}}{A_{min}})}^{2}$
$∴ \frac{I_{max}}{I_{min}} = {(\frac{3}{2})}^{2} = \frac{9}{4}$

Suggest Corrections

Similar questions

4 : 3

7 : 5

(A)

(λ)

(f)

\frac{I_{m a x}}{I_{m i n}} = {(\frac{A_{1} + A_{2}}{A_{1} - A_{2}})}^{2}

25 : 1

Join BYJU'S Learning Program

Explore more

Join BYJU'S Learning Program