Three tuning forks of frequencies 248 Hz, 250 Hz, 252 Hz, are sounded together.The beat frequency is,

Options

A. 2 Hz
B. 4 Hz
C. 6 Hz
D. 8 Hz

Answer

To find the beat frequency when three tuning forks of frequencies 248 Hz, 250 Hz, and 252 Hz are sounded together, we can follow these steps:

### Step 1: Understand the Concept of Beat Frequency
The beat frequency is the difference in frequency between two sound waves. When two tuning forks are sounded together, the beat frequency is given by the absolute difference between their frequencies.

### Step 2: Identify the Frequencies
We have three tuning forks with the following frequencies:
- \( f_1 = 248 \, \text{Hz} \)
- \( f_2 = 250 \, \text{Hz} \)
- \( f_3 = 252 \, \text{Hz} \)

### Step 3: Calculate Beat Frequencies Between Pairs
We will calculate the beat frequencies for each pair of tuning forks:
1. Between \( f_1 \) and \( f_2 \):
\[ \text{Beat frequency (B1)} = |f_1 - f_2| = |248 - 250| = 2 \, \text{Hz} \]

2. Between \( f_2 \) and \( f_3 \):
\[ \text{Beat frequency (B2)} = |f_2 - f_3| = |250 - 252| = 2 \, \text{Hz} \]

3. Between \( f_1 \) and \( f_3 \):
\[ \text{Beat frequency (B3)} = |f_1 - f_3| = |248 - 252| = 4 \, \text{Hz} \]

### Step 4: Determine the Maximum Beat Frequency
The overall beat frequency when all three tuning forks are sounded together is the maximum of the calculated beat frequencies:
\[ \text{Maximum Beat Frequency} = \max(B1, B2, B3) = \max(2 \, \text{Hz}, 2 \, \text{Hz}, 4 \, \text{Hz}) = 4 \, \text{Hz} \]

### Final Answer
The beat frequency when the three tuning forks are sounded together is **4 Hz**.

---