Four tuning forks of frequencies 200,201,204 and 206 Hz are sounded together. The beat frequency will be

Options

A. 6
B. 12
C. 15
D. None of these

Explanation

To find the beat frequency when four tuning forks of frequencies 200 Hz, 201 Hz, 204 Hz, and 206 Hz are sounded together, we can follow these steps:

### Step 1: Understand the concept of beat frequency
The beat frequency is the difference in frequencies between two sound waves. When two tuning forks are sounded together, the number of beats per second is equal to the absolute difference between their frequencies.

### Step 2: Calculate the beat frequencies for each pair of tuning forks
We will calculate the beat frequencies for all possible pairs of the given tuning forks:

1. **Between 200 Hz and 201 Hz:**
\[ |200 - 201| = 1 \text{ Hz} \]

2. **Between 200 Hz and 204 Hz:**
\[ |200 - 204| = 4 \text{ Hz} \]

3. **Between 200 Hz and 206 Hz:**
\[ |200 - 206| = 6 \text{ Hz} \]

4. **Between 201 Hz and 204 Hz:**
\[ |201 - 204| = 3 \text{ Hz} \]

5. **Between 201 Hz and 206 Hz:**
\[ |201 - 206| = 5 \text{ Hz} \]

6. **Between 204 Hz and 206 Hz:**
\[ |204 - 206| = 2 \text{ Hz} \]

### Step 3: List all the beat frequencies calculated
From the calculations above, the beat frequencies are:
- 1 Hz
- 4 Hz
- 6 Hz
- 3 Hz
- 5 Hz
- 2 Hz

### Step 4: Determine the maximum beat frequency
The beat frequency that we hear is the maximum of these calculated beat frequencies.

### Step 5: Find the maximum beat frequency
The maximum beat frequency from our list is:
\[ \text{Maximum Beat Frequency} = 6 \text{ Hz} \]

### Final Answer
Thus, the beat frequency when the four tuning forks are sounded together is **6 Hz**.

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