If a tuning fork of frequency `512Hz` is sounded with a vibrating string of frequency `505.5Hz` the beats produced per sec will be

Options

A. `6`
B. `7`
C. `6.5`
D. Any of the above

Explanation

To solve the problem of finding the number of beats produced per second when a tuning fork of frequency 512 Hz is sounded with a vibrating string of frequency 505.5 Hz, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Frequencies**:
- Let \( n_1 = 512 \, \text{Hz} \) (frequency of the tuning fork)
- Let \( n_2 = 505.5 \, \text{Hz} \) (frequency of the vibrating string)

2. **Calculate the Difference in Frequencies**:
- The formula for the number of beats produced per second is given by the absolute difference between the two frequencies:
\[ \text{Beats per second} = |n_1 - n_2| \]

3. **Substituting the Values**:
- Substitute the values of \( n_1 \) and \( n_2 \):
\[ \text{Beats per second} = |512 \, \text{Hz} - 505.5 \, \text{Hz}| \]

4. **Perform the Calculation**:
- Calculate the difference:
\[ \text{Beats per second} = |512 - 505.5| = |6.5| = 6.5 \, \text{Hz} \]

5. **Conclusion**:
- The number of beats produced per second is \( 6.5 \, \text{Hz} \).

### Final Answer:
The beats produced per second will be **6.5 Hz**.

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