The fundamental frequency of a closed pipe is determined by the length of the pipe. In a closed pipe, the sound wave undergoes a complete reflection at the closed end and a partial reflection at the open end. This causes a standing wave pattern to form inside the pipe.

If the entire pipe is filled with water, the effective length of the pipe increases due to the reflection of the sound wave at the water surface. This results in a decrease in the fundamental frequency.

Given that the fundamental frequency of the closed pipe is 220 Hz, we can determine the length of the pipe using the formula:

λ = 4L

where λ is the wavelength and L is the length of the pipe.

Since the pipe is closed, the fundamental frequency corresponds to the first harmonic, where the wavelength is twice the length of the pipe:

λ1 = 2L

Substituting the given value of the fundamental frequency:

220 = v/λ1

where v is the speed of sound.

We can rearrange the equation to solve for the length of the pipe:

L = v/(2 * 220)

If 1/4 of the pipe is filled with water, the effective length of the pipe becomes 3/4 of the original length. Therefore, the new length of the pipe is:

L' = (3/4) * L

The new fundamental frequency, f', can be determined using the formula:

f' = v/λ'

where λ' is the new wavelength.

Since the pipe is closed, the new fundamental frequency corresponds to the first harmonic, where the new wavelength is twice the new length of the pipe:

λ'1 = 2 * L'

Substituting the values:

f' = v/λ'1
= v/(2 * L')

Substituting the expression for L':

f' = v/(2 * (3/4) * L)
= (4/6) * (v/2L)
= (2/3) * f

where f is the original fundamental frequency.

Given that f = 220 Hz, the new fundamental frequency is:

f' = (2/3) * 220
= 440 Hz

Therefore, the frequency of the first overtone of the pipe, which is twice the fundamental frequency, is:

2 * f' = 2 * 440 Hz
= 880 Hz

Hence, the correct answer is option C) 880 Hz.