Question

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

`y_1 = 5 sin 2pi(75t - 0.25 x)`

`y_2 = 10 sin 2pi(150t - 0.50 x)`

The intensity ratio `"I"_1/"I"_2` of the two waves is ______

Options

• 1 : 2

• 1 : 4

• 1 : 8

• 1 : 16

Answer 1

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

`y_1 = 5 sin 2pi(75t - 0.25 x)`

`y_2 = 10 sin 2pi(150t - 0.50 x)`

The intensity ratio `"I"_1/"I"_2` of the two waves is 1 : 4.

Explanation:

Given equation is

`y_1 = 5 sin 2pi(75t - 0.25 x)` ..................(i)

`y_2 = 10 sin 2pi(150t - 0.50 x)` .................(ii)

General eqⁿ. for the plane progressive wave is given by,

y = A sin 2π `("vt" - "x"/lambda)` .................(iii)

Comparing equations (i), (ii), (iii) we get

A₁ = 5; A₂ = 10

Now, I ∝ A²

⇒ `"I"_1/"I"_2 = "A"_1^2/"A"_2^2`

Substituting A₁ = 5; A₂ = 10, we get

`"I"_1/"I"_2 = 1/4`