Two strings ' X ' and ' Y ' of a guitar produces a beat frequency of 6 Hz . When the tension of the string ' $Y$ ' is increased, the beat frequency is found to be 4 Hz . If the frequency of string ' X ' is 300 Hz , then the original frequency of string ' $Y$ ' is

Given $f_X = 300\text{ Hz}$ produces a beat frequency of $6\text{ Hz}$ with string Y, the original frequency $f_Y$ satisfies $|300 - f_Y| = 6$. This yields possible values $f_Y = 294\text{ Hz}$ or $f_Y = 306\text{ Hz}$.

Increasing tension raises the frequency of string Y. With the new beat frequency reduced to $4\text{ Hz}$, the updated frequency $f_Y'$ satisfies $|300 - f_Y'| = 4$, giving possible values $f_Y' = 296\text{ Hz}$ or $f_Y' = 304\text{ Hz}$.

Since $f_Y' > f_Y$ under increased tension, the case $f_Y = 306\text{ Hz}$ is invalid—neither $296\text{ Hz}$ nor $304\text{ Hz}$ exceeds $306\text{ Hz}$. Only $f_Y = 294\text{ Hz}$ is consistent, as both possible new frequencies exceed $294\text{ Hz}$ and satisfy the beat condition.

The original frequency is therefore $\boxed{294\text{ Hz}}$.