Question

If the ratio of maximum to minimum intensity in beat is 49, then the ratio of amplitudes of two progressive wave trains

• A. 7:1
• B. 4:3
• C. 49:1
• D. 16:9

Answer 1

The correct option is B 4:3

$\frac{I_{max}}{I_{min}}=\frac{(\sqrt{I_1}+\sqrt{I_2}{)}^2}{(\sqrt{I_1}-\sqrt{I_2}{)}^2}=49$

$\frac{(\sqrt{I_1}+\sqrt{I_2})}{(\sqrt{I_1}-\sqrt{I_2})}=7$
$\sqrt{I_1}+\sqrt{I_2}=7(\sqrt{I_1}-\sqrt{I_2})$

$\frac{\sqrt{I_1}}{\sqrt{I_2}}=\frac{4}{3}$

$\frac{a}{b}=\frac{4}{3}$

Here, $a=\sqrt{I_1}$ and $b=\sqrt{I_2}$, where a and b are the amplitudes of the two progressive waves.