Assertion When a wave travels from a denser to a rarer medium, its amplitude increases.
Reason In a rarer medium, speed of wave is more

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason is not correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Explanation

To solve the assertion-reason question, we will analyze both the assertion and the reason step by step.

### Step 1: Understanding the Assertion
The assertion states that when a wave travels from a denser medium to a rarer medium, its amplitude increases.

- **Denser Medium**: This medium has a higher density, which typically means that the speed of the wave is lower compared to a rarer medium.
- **Rarer Medium**: This medium has a lower density, which allows the wave to travel faster.

### Step 2: Analyzing the Reason
The reason provided states that in a rarer medium, the speed of the wave is greater.

- This is a fundamental property of waves: they generally travel faster in less dense (rarer) media compared to denser media.

### Step 3: Relating Amplitude and Velocity
We need to establish a relationship between amplitude and velocity when transitioning from one medium to another. The relationship can be expressed as:

\[ \frac{A_2}{A_1} = \frac{2V_2}{V_1 + V_2} \]

Where:
- \(A_1\) = Amplitude in the denser medium
- \(A_2\) = Amplitude in the rarer medium
- \(V_1\) = Velocity in the denser medium
- \(V_2\) = Velocity in the rarer medium

### Step 4: Comparing Velocities
From the properties of wave propagation, we know that:

\[ V_2 > V_1 \]

This indicates that the velocity in the rarer medium is greater than that in the denser medium.

### Step 5: Conclusion on Amplitude
Since \(V_2\) is greater than \(V_1\), substituting this into the amplitude relationship shows that:

\[ A_2 > A_1 \]

Thus, the amplitude of the wave in the rarer medium is greater than that in the denser medium.

### Final Conclusion
Both the assertion and the reason are true, and the reason correctly explains the assertion. Therefore, the correct answer is that both the assertion and reason are true, and the reason is the correct explanation for the assertion.