Question

Which statements are true about wave propagation through a medium:
A. Frequency changes in a non-linear medium but remains constant in a linear medium.
B. Frequency changes in a linear medium but remains constant in a non-linear medium.
C. R + T = 1, where R is the reflection coefficient and T is the transmission coefficient
D. R + T $>$ 1, where R is the reflection coefficient and T is the transmission coefficient
Choose the correct answer from the options given below:

• A. A and D only
• B. A and C only
• C. A, B, C and D
• D. B, C and D only

Hint:

A key principle in wave physics is that frequency is determined by the source and does not change when the wave enters a new \textit{linear} medium (only wavelength and speed change). The law R + T = 1 is a direct consequence of energy conservation at a boundary, a fundamental concept in physics.

Answer 1

The Correct Option is B

Step 1: Concept Overview:
This question assesses wave propagation principles, focusing on frequency behavior in different media and energy conservation at interfaces.
Step 2: Detailed Analysis:
Statements A and B:
Wave frequency is source-dependent. In a linear medium, the frequency remains constant because the medium responds proportionally to the wave. Conversely, a non-linear medium exhibits properties dependent on the wave's amplitude, potentially generating new frequencies like harmonics. Thus, frequency can change in a non-linear medium but not in a linear one.
Statement A is correct; Statement B is incorrect.
Statements C and D:
The reflection coefficient (R) is the ratio of reflected to incident wave intensity (\(I_r/I_i\)). The transmission coefficient (T) is the ratio of transmitted to incident wave intensity (\(I_t/I_i\)).
Energy conservation dictates that the incident wave's total energy at an interface equals the sum of the reflected and transmitted wave energies, assuming no energy absorption.
\[ I_i = I_r + I_t \]
Dividing by \(I_i\) yields:
\[ 1 = \frac{I_r}{I_i} + \frac{I_t}{I_i} \implies 1 = R + T \]
Therefore, statement C is correct, while statement D, which contradicts energy conservation, is incorrect.
Step 3: Conclusion:
Statements A and C are correct.