An open organ pipe (i. e., a pipe open at both ends) of length l0 has a fundamental frequency f0. part a if the organ pipe is cut in half, what is the new fundamental frequency?

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.

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