A tuning fork produces 7 beats/s with a tuning fork of frequency 248Hz. Unknown fork is now loaded and 7 beats/s are still heard. The frequency of unknown fork was

Options

A. 241 Hz
B. 248 Hz
C. 255 Hz
D. 234 Hz

Answer

To solve the problem step by step, we need to determine the frequency of the unknown tuning fork based on the information given about the beats produced.

### Step 1: Understand the concept of beats
The beat frequency is defined as the absolute difference between the frequencies of two tuning forks. If two tuning forks produce beats, the beat frequency (n) can be expressed as:
\[ n = |f_1 - f_2| \]
where \( f_1 \) is the frequency of the first tuning fork and \( f_2 \) is the frequency of the second tuning fork.

### Step 2: Identify the known values
From the problem, we know:
- The frequency of the known tuning fork \( f_1 = 248 \, \text{Hz} \)
- The beat frequency \( n = 7 \, \text{beats/s} \)

### Step 3: Set up the equation for the beat frequency
Using the formula for beat frequency:
\[ |f_1 - f_2| = 7 \]
This can be rewritten as two possible equations:
1. \( f_2 - f_1 = 7 \)
2. \( f_1 - f_2 = 7 \)

### Step 4: Solve for \( f_2 \)
Since the problem states that the unknown fork is loaded and still produces 7 beats/s, we can conclude that the frequency of the unknown fork increases when loaded. Therefore, we will use the first equation:
\[ f_2 - 248 = 7 \]

Now, we can solve for \( f_2 \):
\[ f_2 = 248 + 7 \]
\[ f_2 = 255 \, \text{Hz} \]

### Step 5: Conclusion
The frequency of the unknown tuning fork is:
\[ f_2 = 255 \, \text{Hz} \]

### Final Answer
The frequency of the unknown fork was **255 Hz**.

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