A girl stops singing a pure note. She is surprised to hear an echo of higher frequency, i.e., a higher musical pitch. Then :

A. there could be some warm air between the girl and the reflecting surface
B. there could be two identical fixed reflecting surfaces, one half a wavelengths of the sound wave away from the other
C. the girl could be moving towards a fixed reflector
D. the reflector could be moving towards the girl

Options

A. there could be some warm air between the girl and the reflecting surface
B. there could be two identical fixed reflecting surfaces, one half a wavelengths of the sound wave away from the other
C. the girl could be moving towards a fixed reflector
D. the reflector could be moving towards the girl

Answer

To solve the question, we need to analyze the situation described and the possible reasons for the girl hearing an echo of higher frequency after she stops singing. Let's go through the options one by one.

### Step-by-Step Solution:

1. **Understanding the Scenario**:
- The girl stops singing a pure note and hears an echo of a higher frequency. This indicates that the frequency of the sound wave that returns to her is greater than the frequency of the sound she originally produced.

2. **Analyzing Option A**:
- **Statement**: There could be some warm air between the girl and the reflecting surface.
- **Analysis**: Sound travels faster in warm air than in cooler air. However, if both the original sound and the echo travel through the same medium (warm air), the frequency of the echo would not be greater than the original frequency. Thus, this option is **incorrect**.

3. **Analyzing Option B**:
- **Statement**: There could be two identical fixed reflecting surfaces, one half a wavelength of the sound wave away from the other.
- **Analysis**: The frequency of sound does not depend on the distance between reflecting surfaces. The frequency remains constant regardless of the distance. Therefore, this option is also **incorrect**.

4. **Analyzing Option C**:
- **Statement**: The girl could be moving towards a fixed reflector.
- **Analysis**: If the girl is moving towards the reflecting surface, the frequency of the sound wave that she hears (the echo) will be increased due to the Doppler effect. The frequency of the echo can be calculated using the Doppler effect formula, which shows that the frequency increases when the source moves towards the observer. Thus, this option is **correct**.

5. **Analyzing Option D**:
- **Statement**: The reflector could be moving towards the girl.
- **Analysis**: Similar to option C, if the reflecting surface is moving towards the girl, the frequency of the echo will also be increased due to the Doppler effect. This means that the girl will hear a higher frequency echo. Therefore, this option is also **correct**.

### Conclusion:
The correct answers are:
- **C. The girl could be moving towards a fixed reflector.**
- **D. The reflector could be moving towards the girl.**