(A): When an observer in motion 'passes by a stationary source the apparent frequency heard first continuously increases and then continously decreases.
(R) : Apparent change in wavelength is not responsible for the change in frequency.

Options

A. Both 'A' and 'R' are true and 'R' is the correct, explanation of 'A'.
B. Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'
C. A' is true and 'R' is false
D. Both 'A' and 'R' are false

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) given in the problem.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that when an observer in motion passes by a stationary source, the apparent frequency heard first continuously increases and then continuously decreases.
- This phenomenon can be explained using the Doppler effect, which describes how the frequency of a wave changes for an observer moving relative to the source of the wave.

2. **Analyzing the Motion of the Observer**:
- When the observer moves towards the stationary source, the sound waves get compressed, leading to an increase in the frequency heard by the observer.
- As the observer passes the source and starts moving away, the sound waves get stretched, resulting in a decrease in the frequency.

3. **Conclusion on Assertion (A)**:
- The assertion is true because it accurately describes the behavior of apparent frequency as the observer moves towards and then away from the source.

4. **Understanding the Reason (R)**:
- The reason states that the apparent change in wavelength is not responsible for the change in frequency.
- According to the Doppler effect, the frequency change is due to the relative motion between the source and the observer, not due to a change in the wavelength of the sound produced by the source.

5. **Analyzing the Reason (R)**:
- The frequency \( f \) can be expressed as \( f = \frac{v}{\lambda} \), where \( v \) is the speed of sound and \( \lambda \) is the wavelength.
- In this case, while the observer's motion affects the frequency, the wavelength remains constant for a stationary source. Thus, the change in frequency is due to the change in the relative velocity of the observer and the source.

6. **Conclusion on Reason (R)**:
- The reason is also true, but it does not correctly explain the assertion because the change in frequency is primarily due to the change in relative velocity, not a change in wavelength.

7. **Final Evaluation**:
- Both A and R are true, but R is not the correct explanation of A. Therefore, the correct option is that both A and R are true, but R is not the correct explanation of A.

### Final Answer:
Both A and R are true, but R is not the correct explanation of A.

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