Aguitar string produces 4 beats/second when sounded with
a250hz tuning fork and 9 beats/second when sounded with a 255
hztuning fork. what is the vibrational frequency?

In first case vibrational frequency will be 246 Hz and 254 Hz

In second case vibrational frequency will be 264 Hz and 246 Hz

Explanation:

We have given a guitar produces 4 beats per second when sounded with 250 Hz and produce 9 beats per second when sounded with 255 Hz

Expression of beat frequency is

Here is vibrational frequency

So

For second case