Question

The intensity is due to 2 sources of sound i0 and 4i. What is the intensity at a point where the phase diffrent between 2 waves is

Answer 1

When two sources of sounds interfere with each other, the two displacements or Amplitudes are algebraically/vectorially added at any point.

Given Intensity of wave 1:  I₀               Intensity of wave 2:  4 *I₀
Amplitude of wave1: A₀ = a√I₀ , for a constant a 
Amplitude of wave 2 = 2 * A₀ as amplitude is proportional to square root of intensity.

Intensity after interference : I = I₁ + I₂ + 2 √(I₁ I₂)  * CosФ
           where Ф = phase difference

1)  Ф = Ф or 2 n π
         I = I₀ + 4 I₀ + 2 * (2 I₀) * Cos Ф  = 9 I₀ 
           Amplitude = 3 times that of wave with intensity I₀

2) Ф = π, 
         I = I₀ + 4 I₀ + 2 (2 I₀) (-1) = I₀

3) Ф = π/2
         I = I₀ + 4 I₀ + 0   = 5 I₀