If a note was "fretted", by reducing the length of the string to 0.25 m, then the lowest frequency note this string could play is?

in Hertz

I am not certain of the term fretted. The lowest frequency will be the longest wavelength, so that normally means the length of the string will be 1/2 wavelength at the lowest frequency.

I do not understand how to solve the problem still.

To find the lowest frequency note that a string can play when fretted, we need to consider the relationship between frequency, wavelength, and string length. Fretting refers to the act of reducing the playable length of a string by pressing it against a fret on a musical instrument.

In this case, if the length of the string when fretted is 0.25 m, we can consider this as the new length of the string. The general formula for the fundamental frequency of a vibrating string is:

f = v / (2L)

where:
f is the frequency (in Hertz),
v is the speed of the wave (which is usually the speed of sound, 343 m/s in air), and
L is the length of the string.

Given that the new length of the string is 0.25 m, we can substitute this value into the formula to find the frequency:

f = 343 / (2 * 0.25)

f = 343 / 0.5

f ≈ 686 Hz

Therefore, the lowest frequency note this string could play when fretted is approximately 686 Hz.