A tuning fork of frequency 512 Hz produces 6 beats per sec. with vibrating string of an instrument. On increasing the tension in the string, the beat frequency reduces to 3 beats/sec. Find the original frequency of the instrument.

Explanation

To solve the problem, we need to determine the original frequency of the instrument based on the information provided about the beats produced when the tuning fork and the instrument are played together.

### Step-by-Step Solution:

1. **Understanding Beat Frequency**:
The beat frequency is the absolute difference between the frequencies of two sound sources. In this case, we have a tuning fork with a frequency of 512 Hz and an instrument whose frequency we need to find, denoted as \( f_2 \).

2. **Initial Beat Frequency**:
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