An open pipe, 0.29 m long, vibrates in the second overtone with a frequency of 1,227 Hz. In this situation, the fundamental frequency of the pipe, in SI units, is closest to:

f = 409 Hz

Explanation:

We have,

Length of the open organ pipe, l = 0.29 m

Frequency of vibration of second overtone,

It is required to find the fundamental frequency of the pipe. For the open organ pipe, the frequency of second overtone is given by :

v is speed of sound

Let f is the fundamental frequency. It is given by :

The relation between f and f₂ can be written as :

So, the fundamental frequency of the pipe is 409 Hz.              

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