On sounding two tuning forks A and B together 5 beats per second are produced. On filling A slightly, the number of beats per second becomes 2. If the frequency of the A is 384 Hz. Then the frequency of B will be -

Options

A. 319 Hz
B. 314 Hz
C. 389 Hz
D. 334 Hz

Answer

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

### Step 1: Understand the concept of beats
When two tuning forks are sounded together, the phenomenon of beats occurs due to the interference of sound waves from the two sources. The number of beats per second is equal to the absolute difference in their frequencies.

### Step 2: Set up the equations based on the information given
Let:
- Frequency of tuning fork A (FA) = 384 Hz
- Frequency of tuning fork B (FB) = unknown
- Number of beats when both forks are sounded together = 5 beats/sec

From the information given, we can write the first equation:
\[ |FB - FA| = 5 \]

### Step 3: Solve for FB
Substituting the value of FA:
\[ |FB - 384| = 5 \]

This gives us two possible equations:
1. \( FB - 384 = 5 \) (1)
2. \( 384 - FB = 5 \) (2)

### Step 4: Solve the first equation
From equation (1):
\[ FB = 384 + 5 \]
\[ FB = 389 \text{ Hz} \]

### Step 5: Solve the second equation
From equation (2):
\[ 384 - FB = 5 \]
\[ FB = 384 - 5 \]
\[ FB = 379 \text{ Hz} \]

### Step 6: Analyze the effect of filling fork A
When fork A is filled slightly, its frequency increases. The problem states that the number of beats per second then becomes 2. This means:
\[ |FB - (FA + \Delta f)| = 2 \]
Where \( \Delta f \) is the increase in frequency of fork A.

Since we know that the frequency of A increases, we can conclude that:
- If FB = 389 Hz, then after filling A, the frequency of A will be greater than 384 Hz, leading to a decrease in the number of beats (from 5 to 2).
- If FB = 379 Hz, the frequency of A would need to increase to create a situation where the beats decrease to 2, which is not possible since it would require a frequency less than 384 Hz.

### Conclusion
Thus, the only valid solution is:
\[ FB = 389 \text{ Hz} \]

### Final Answer
The frequency of tuning fork B is 389 Hz.

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