Two sound waves having the same wavelength 1 and same frequency but with intensities 9 I0 and 4 I0 are interfering. When the path difference between the waves is (λ/4) the resulting intensity is nI 0. What is the value of n ?

Question

Two sound waves having the same wavelength 1 and same frequency but with intensities 9 I0 and 4 I0 are interfering. When the path difference between the waves is (λ/4) the resulting intensity is nI 0. What is the value of n ? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

φ=(2 π/λ) × Δ x =(2 π/λ) × (λ/4)=(π/2) I = I 1+ I 2+2 √ I 1 I 2 cos φ 9 I 0+4 I 0=13 I 0

Q. Two sound waves having the same wavelength $1$ and same frequency but with intensities $9 I_{0}$ and $4 I_{0}$ are interfering. When the path difference between the waves is $\frac{λ}{4}$ the resulting intensity is $n I_{0}$ . What is the value of $n$ ?

$ϕ = \frac{2 π}{λ} \times Δ x = \frac{2 π}{λ} \times \frac{λ}{4} = \frac{π}{2}$
$I = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ$
$9 I_{0} + 4 I_{0} = 13 I_{0}$

Q. Two sound waves having the same wavelength 1 and same frequency but with intensities 9I0​ and 4I0​ are interfering. When the path difference between the waves is 4λ​ the resulting intensity is nI0​. What is the value of n ?

ϕ=λ2π​×Δx=λ2π​×4λ​=2π​ I=I1​+I2​+2I1​I2​​cosϕ 9I0​+4I0​=13I0​

Q. Two sound waves having the same wavelength $1$ and same frequency but with intensities $9 I_{0}$ and $4 I_{0}$ are interfering. When the path difference between the waves is $\frac{λ}{4}$ the resulting intensity is $n I_{0}$ . What is the value of $n$ ?

$ϕ = \frac{2 π}{λ} \times Δ x = \frac{2 π}{λ} \times \frac{λ}{4} = \frac{π}{2}$
$I = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ$
$9 I_{0} + 4 I_{0} = 13 I_{0}$