A tuning fork A of frequency 384 Hz gives 6 beats in 2 second when sounded with another tuning fork B. The frequency of B could be ?

Question

Accepted Answer

To determine the frequency of tuning fork B, we need to consider the concept of beats. Beats occur when two sound waves of slightly different frequencies interfere with each other, resulting in a fluctuating sound intensity. The beat frequency is equal to the absolute difference between the two frequencies.

Given:
- Frequency of tuning fork A = 384 Hz
- Number of beats in 2 seconds = 6

The beat frequency is calculated as the number of beats per second. Therefore, the beat frequency is:
$$ \text{Beat frequency} = \frac{6 \text{ beats}}{2 \text{ seconds}} = 3 \text{ Hz} $$

This means that the frequency of tuning fork B could either be 3 Hz higher or 3 Hz lower than the frequency of tuning fork A. Thus, the possible frequencies for tuning fork B are:
- $ 384 \text{ Hz} + 3 \text{ Hz} = 387 \text{ Hz} $
- $ 384 \text{ Hz} - 3 \text{ Hz} = 381 \text{ Hz} $

Therefore, the frequency of tuning fork B could be either 381 Hz or 387 Hz, which corresponds to Option 2: 381, 387.

Now, let's explain why the other options are incorrect:

1. **Option 1: 382, 386**
   - If the frequency of B were 382 Hz, the beat frequency would be $ |384 - 382| = 2 \text{ Hz} $.
   - If the frequency of B were 386 Hz, the beat frequency would be $ |384 - 386| = 2 \text{ Hz} $.
   - Neither of these beat frequencies matches the given beat frequency of 3 Hz.

2. **Option 3: 378, 390**
   - If the frequency of B were 378 Hz, the beat frequency would be $ |384 - 378| = 6 \text{ Hz} $.
   - If the frequency of B were 390 Hz, the beat frequency would be $ |384 - 390| = 6 \text{ Hz} $.
   - Both of these beat frequencies are incorrect as they do not match the given beat frequency of 3 Hz.

3. **Option 4: 380, 384**
   - If the frequency of B were 380 Hz, the beat frequency would be $ |384 - 380| = 4 \text{ Hz} $.
   - If the frequency of B were 384 Hz, the beat frequency would be $ |384 - 384| = 0 \text{ Hz} $.
   - Neither of these beat frequencies matches the given beat frequency of 3 Hz.

In conclusion, Option 2 is the only choice that provides frequencies (381 Hz and 387 Hz) which result in the correct beat frequency of 3 Hz, thereby justifying it as the correct answer.