Two sounds A and B are of same amplitudes, same wave forms but of frequencies f and 2f respectively. Then :

Options

A. B differ in quality from A
B. B is grave, A is shrill
C. B is shrill, A is grave
D. B is louder than A.

Explanation

To solve the question regarding the sounds A and B, we need to analyze the properties of sound, specifically amplitude and frequency.

### Step-by-Step Solution:

1. **Identify the Properties of Sound**:
- Sound has two main properties that we need to consider: amplitude and frequency.
- Amplitude affects the loudness of the sound, while frequency affects the pitch of the sound.

2. **Given Information**:
- Both sounds A and B have the same amplitude, which means they will have the same loudness.
- Sound A has a frequency of \( f \) and sound B has a frequency of \( 2f \).

3. **Analyze Loudness**:
- Since both sounds have the same amplitude, they will be perceived as having the same loudness. Therefore, we can conclude that:
- **B is not louder than A**. This eliminates option 4.

4. **Analyze Pitch**:
- Frequency determines the pitch of the sound. A higher frequency results in a higher pitch (more shrill sound).
- Since the frequency of sound B (which is \( 2f \)) is greater than the frequency of sound A (which is \( f \)), we can conclude that:
- **Sound B is more shrill than sound A**.

5. **Determine Quality of Sound**:
- The term "grave" refers to a lower pitch sound, while "shrill" refers to a higher pitch sound.
- Therefore, since B has a higher frequency, it will be shriller, and A, having a lower frequency, will be grave.

6. **Conclusion**:
- From the analysis, we can conclude that:
- Sound B is shrill, and sound A is grave.
- Thus, the correct option is that B is shrill and A is grave.

### Final Answer:
**Option 3 is correct: B is shrill, A is grave.**

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