A source of sound with adjustable frequency produces 2. beats per second with a tuning fork when its frequency is either 476 Hz or 480 Hz. What is the frequency of the tuning fork ?

Explanation

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

### Step 1: Understand the concept of beats
When two sound waves of slightly different frequencies interfere, they produce a phenomenon known as beats. The number of beats per second (n) is equal to the absolute difference between the two frequencies.

### Step 2: Set up the equations
We are given that the sound source produces 2 beats per second (n = 2) with two frequencies: 476 Hz and 480 Hz. We can express this mathematically as:
1. |µ - 476| = 2
2. |µ - 480| = 2

Where µ is the frequency of the tuning fork.

### Step 3: Solve the first equation
From the first equation, we can have two cases:
- Case 1: µ - 476 = 2
- µ = 476 + 2 = 478 Hz
- Case 2: 476 - µ = 2
- µ = 476 - 2 = 474 Hz

### Step 4: Solve the second equation
From the second equation, we can also have two cases:
- Case 1: µ - 480 = 2
- µ = 480 + 2 = 482 Hz
- Case 2: 480 - µ = 2
- µ = 480 - 2 = 478 Hz

### Step 5: Find the common solution
Now we compare the results from both equations:
- From the first equation, we found µ = 478 Hz or µ = 474 Hz.
- From the second equation, we found µ = 478 Hz or µ = 482 Hz.

The only common frequency from both sets of results is:
- µ = 478 Hz

### Conclusion
Thus, the frequency of the tuning fork is **478 Hz**.

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