First slide

Superposition of waves

Question

The superposing waves are represented by the following equations :
$y_{1} = 5 \sin 2 π (10 t - 0 .1 x), y_{2} = 10 \sin 2 π (20 t - 0 .2 x)$
Ratio of intensities $\frac{I_{\max}}{I_{\min}}$ will be

Easy

A

1
B

9
C

4
D

16

Solution

$a_{1} = 5, a_{2} = 10 \Rightarrow \frac{I_{\max}}{I_{\min}} = \frac{{(a_{1} + a_{2})}^{2}}{{(a_{1} - a_{2})}^{2}} = {(\frac{5 + 10}{5 - 10})}^{2} = \frac{9}{1}$

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