Two tuning forks A and B vibrating simultaneously produces, 5 beats. Frequency of B is 512. It is seen that if one arm of A is filed, then the number of beats increases. Frequency of A will be

Options

A. 502
B. 507
C. 517
D. 522

Explanation

To find the frequency of tuning fork A, we can follow these steps:

### Step 1: Understand the concept of beats
When two tuning forks of different frequencies are sounded together, they produce beats, which is the periodic variation in sound intensity. The number of beats per second is equal to the absolute difference in their frequencies.

### Step 2: Set up the equation for beats
Let the frequency of tuning fork A be \( f_A \) and the frequency of tuning fork B be \( f_B = 512 \) Hz. Given that the two forks produce 5 beats, we can express this as:
\[ |f_A - f_B| = 5 \]
This can be rewritten in two possible equations:
1. \( f_A - f_B = 5 \)
2. \( f_B - f_A = 5 \)

### Step 3: Solve the first equation
Using the first equation:
\[ f_A - 512 = 5 \]
Adding 512 to both sides gives:
\[ f_A = 512 + 5 = 517 \text{ Hz} \]

### Step 4: Solve the second equation
Using the second equation:
\[ 512 - f_A = 5 \]
Rearranging gives:
\[ f_A = 512 - 5 = 507 \text{ Hz} \]

### Step 5: Analyze the effect of filing one arm of A
The problem states that filing one arm of A increases the number of beats. This means that the frequency of A must be increasing. If \( f_A \) were 507 Hz, filing would decrease the frequency, leading to fewer beats, which contradicts the information given.

### Conclusion
Thus, the only valid solution that satisfies the condition of increasing beats when filing one arm of A is:
\[ f_A = 517 \text{ Hz} \]

### Final Answer
The frequency of tuning fork A is **517 Hz**.

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