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: Understanding the Concept:
This question tests fundamental principles of wave propagation, specifically how frequency behaves in different media and the conservation of energy at an interface.
Step 2: Detailed Explanation:
Statement A and B:
The frequency of a wave is determined by its source. When a wave passes through a linear medium, the medium responds proportionally to the wave's oscillations, so the frequency remains constant. In a non-linear medium, the medium's properties depend on the wave's amplitude. This non-linear response can generate new frequencies, such as harmonics (multiples of the original frequency). Therefore, the frequency can change in a non-linear medium but remains constant in a linear one.
Statement A is correct, and statement B is incorrect.
Statement C and D:
The reflection coefficient (R) is the ratio of reflected wave intensity to incident wave intensity (\(I_r/I_i\)). The transmission coefficient (T) is the ratio of transmitted wave intensity to incident wave intensity (\(I_t/I_i\)).
According to the principle of conservation of energy, the total energy of the incident wave at an interface must equal the sum of the energies of the reflected and transmitted waves, assuming there is no absorption of energy at the interface.
\[ I_i = I_r + I_t \]
Dividing the entire equation by \(I_i\), we get:
\[ 1 = \frac{I_r}{I_i} + \frac{I_t}{I_i} \implies 1 = R + T \]
Therefore, statement C is correct, and statement D, which violates the conservation of energy, is incorrect.
Step 3: Final Answer:
The correct statements are A and C.