What is the reflected intensity from a boundary between two materials if the incident intensity is 1 mW/cm² and the impedances are 25 and 75?

• A. 0.25 mW/cm²
• B. 0.33 mW/cm²
• C. 0.50 mW/cm²
• D. 1.0 mW/cm²

Answer: (A)

To determine the reflected intensity at the boundary between two materials with different acoustic impedances, we can use the formula for the reflection coefficient ( R ), which is defined as:

[

R = \left( \frac{Z_2 - Z_1}{Z_2 + Z_1} \right)^2

]

where ( Z_1 ) is the impedance of the first medium and ( Z_2 ) is the impedance of the second medium. The intensities of the reflected and incident waves are related by:

[

I_r = I_i \cdot R

]

In this case, the impedances are given as 25 for the first material and 75 for the second material. By substituting these values into the reflection coefficient formula, we can calculate:

[

R = \left( \frac{75 - 25}{75 + 25} \right)^2 = \left( \frac{50}{100} \right)^2 = (0.5)^2 = 0.25

]

Now, to find the reflected intensity ( I_r ), we need to multiply the incident intensity ( I_i ) of 1 mW/cm² by the