The points of the prongs of a tuning fork B originally in unison with a tuning fork A of frequency 384 are filed and the fork produces 3 beats per second, when sounded together with A. What is the pitch of B after filing ?

Answer

To solve the problem, we need to determine the frequency of tuning fork B after it has been filed, given that it produces 3 beats per second when sounded together with tuning fork A, which has a frequency of 384 Hz.

### Step-by-Step Solution:

1. **Understand the Beat Frequency Concept**:
- When two tuning forks are sounded together, the beat frequency is the absolute difference between their frequencies.
- The formula for beat frequency is given by:
\[ f_{\text{beat}} = |f_A - f_B| \]
- Here, \( f_A \) is the frequency of tuning fork A, and \( f_B \) is the frequency of tuning fork B.

2. **Identify Known Values**:
- The frequency of tuning fork A, \( f_A = 384 \) Hz.
- The beat frequency, \( f_{\text{beat}} = 3 \) Hz.

3. **Set Up the Equation**:
- From the beat frequency formula, we have:
\[ |384 - f_B| = 3 \]

4. **Solve for \( f_B \)**:
- This absolute value equation gives us two possible scenarios:
1. \( 384 - f_B = 3 \)
2. \( f_B - 384 = 3 \)

- For the first case:
\[ 384 - f_B = 3 \implies f_B = 384 - 3 = 381 \text{ Hz} \]

- For the second case:
\[ f_B - 384 = 3 \implies f_B = 384 + 3 = 387 \text{ Hz} \]

5. **Determine the Correct Frequency**:
- Since the problem states that the prongs of tuning fork B are filed, this typically decreases the frequency of the fork. Therefore, we choose the lower frequency:
\[ f_B = 381 \text{ Hz} \]

6. **Conclusion**:
- The pitch of tuning fork B after filing is 381 Hz.

### Final Answer:
The pitch of tuning fork B after filing is **381 Hz**.