Two waves represented by the following equations are travelling in the same medium y1=5sin 2π (75 t - 0 .25 x) y2=10sin 2π (150 t - 0.50 x) The intensity ratio (I1/I2) of the two waves is

Question

Two waves represented by the following equations are travelling in the same medium y1=5sin 2π (75 t - 0 .25 x) y2=10sin 2π (150 t - 0.50 x) The intensity ratio (I1/I2) of the two waves is (A) 1:2 (B) 1:4 (C) 1:8 (D) 1:16

Tardigrade Admin · Accepted Answer

I=(1/2)ÏÏ2A2v (I1/I2)=(ω 12 A12/ω 22 A22) (I1/I2)=((75/150))2((5/10))2 (I1/I2)=(1/16)

Q. Two waves represented by the following equations are travelling in the same medium

$y_{1} = 5 s in 2 π (75 t - 0.25 x)$

$y_{2} = 10 s in 2 π (150 t - 0.50 x)$

The intensity ratio $\frac{I _{1}}{I _{2}}$ of the two waves is

$1 : 2$

$1 : 4$

$1 : 8$

$1 : 16$

$I = \frac{1}{2} ρ ω^{2} A^{2} v$
$\frac{I _{1}}{I _{2}} = \frac{ω _{1}^{2} A _{1}^{2}}{ω _{2}^{2} A _{2}^{2}}$
$\frac{I _{1}}{I _{2}} = (\frac{75}{150})^{2} (\frac{5}{10})^{2}$
$\frac{I _{1}}{I _{2}} = \frac{1}{16}$

Q. Two waves represented by the following equations are travelling in the same medium y1​=5sin2π(75t−0.25x) y2​=10sin2π(150t−0.50x) The intensity ratio I2​I1​​ of the two waves is

1:2

1:4

1:8

1:16