Tuning fork A when sounded with a tuning for B of frequency 480 Hz gives 5 beats per second. When the prongs of A are loaded with wax, it gives 3 beats per second. The original frequency of A is

Options

A. 475Hz
B. 485 Hz
C. 483 Hz
D. 477 Hz

Explanation

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

### Step 1: Understand the Beat Frequency
The beat frequency is the difference between the frequencies of two tuning forks. When tuning fork A is sounded with tuning fork B (which has a frequency of 480 Hz), they produce a beat frequency of 5 beats per second. This means that the frequency of tuning fork A (let's denote it as f_A) can either be:
- f_A = 480 Hz - 5 Hz = 475 Hz (if A is lower than B)
- f_A = 480 Hz + 5 Hz = 485 Hz (if A is higher than B)

### Step 2: Analyze the Effect of Loading Wax
When the prongs of tuning fork A are loaded with wax, its frequency decreases. The problem states that with the wax, the beat frequency becomes 3 beats per second.

### Step 3: Determine the New Frequencies
If the original frequency of A is 475 Hz, the new frequency after loading with wax would be less than 475 Hz. The possible frequencies would be:
- f_A (after wax) < 475 Hz

The beat frequency with fork B (480 Hz) would then be:
- Beat frequency = 480 Hz - f_A (after wax)
Since f_A (after wax) < 475 Hz, the beat frequency would be greater than 5 Hz, which contradicts the given information of 3 beats per second.

Now, if we assume the original frequency of A is 485 Hz, then after loading with wax, the frequency would be:
- f_A (after wax) < 485 Hz

The beat frequency with fork B would then be:
- Beat frequency = 480 Hz - f_A (after wax)

If we denote the new frequency as f_A (after wax) = 485 Hz - x (where x is a positive value), the beat frequency becomes:
- Beat frequency = 480 Hz - (485 Hz - x) = x - 5 Hz

For the beat frequency to be 3 Hz:
- x - 5 = 3
- x = 8

This means the new frequency of A after loading with wax is:
- f_A (after wax) = 485 Hz - 8 Hz = 477 Hz

### Step 4: Conclusion
Since the original frequency of tuning fork A must be 485 Hz to satisfy the conditions of the problem, we conclude:
- The original frequency of tuning fork A is **485 Hz**.