A tuning fork A is being tested using an accurate oscillator. It is found that they produce 2 beats per second when the oscillator reads 514 Hz and 6 beats per second when it reads 510 Hz. The actual frequency of the fork in Hz is

Options

A. 512 Hz
B. 504 Hz
C. 516 Hz
D. 510 Hz

Explanation

To find the actual frequency of the tuning fork A, we can use the information given about the beats produced with the oscillator at different frequencies.

### Step-by-Step Solution:

1. **Understanding Beats**:
The number of beats per second is equal to the absolute difference between the frequencies of the two sources. If the tuning fork produces 2 beats per second with the oscillator at 514 Hz, it means:
\[ |f - 514| = 2 \]
This gives us two possible equations:
\[ f = 514 + 2 = 516 \quad \text{(1)} \]
\[ f = 514 - 2 = 512 \quad \text{(2)} \]

2. **Using the Second Condition**:
When the oscillator reads 510 Hz, it produces 6 beats per second:
\[ |f - 510| = 6 \]
This gives us two more possible equations:
\[ f = 510 + 6 = 516 \quad \text{(3)} \]
\[ f = 510 - 6 = 504 \quad \text{(4)} \]

3. **Finding Common Frequency**:
Now, we need to find the common frequency from the results of equations (1), (2), (3), and (4):
- From (1), we have \( f = 516 \)
- From (2), we have \( f = 512 \)
- From (3), we have \( f = 516 \)
- From (4), we have \( f = 504 \)

The only common frequency from these equations is \( f = 516 \).

4. **Conclusion**:
Therefore, the actual frequency of the tuning fork A is:
\[ \boxed{516 \text{ Hz}} \]