Answer:
The fundamental frequency is
Explanation:
For an open-open pipe, the wavelength of the fundamental mode of vibration is equal to twice the length of the pipe:
where L is the length of the pipe.
Moreover, from the wave equation we know that the frequency of the fundamental mode is inversely proportional to the wavelength, according to:
where
f is the frequency
v is the speed of the wave
is the wavelength
Combining the two equations, we get
this means that the fundamental frequency in an open organ pipe is inversely proportional to the length of the pipe.
Here, the pipe is cut in a half, so the new length is
Therefore, since the speed of the sound wave does not change (it depends only on the medium), the new fundamental frequency will be:
So, the fundamental frequency has doubled.