Question

Two waves represented by the following equations are travelling in the same medium
$y_1=5\sin 2\pi \left(75t-0.25X\right),$
$y_2=10\sin 2\pi \left(150t-0.50X\right)$
The intensity ratio $I_1/I_2$ of the two waves is $:-$

• A. $1:2$
• B. $1:4$
• C. $1:8$
• D. $1:16$

Answer 1

The correct option is B $1:4$

Given,

$y_1=5sin2\pi (75t-0.25x)$

$y_2=10sin2\pi (150t-0.50x)$

From the above equation,

$a_1=5,a_2=10$

As we know that the intensity of wave is square of the amplitude of the wave.

$I\propto a^2$

so, $\frac{I_1}{I_2}=\frac{a_1^2}{a_2^2}$

$\frac{I_1}{I_2}=\frac{25}{100}=\frac{1}{4}$

$I_1:I_2=1:4$

The correct option is B.