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The fundamental of an organ pipe that is closed at one end

Chapter 14, Problem 92GP

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QUESTION:

Problem 92GP

The fundamental of an organ pipe that is closed at one end and open at the other end is 261.6 Hz (middle C). The second harmonic of an organ pipe that is open at both ends has the same frequency. What are the lengths of these two pipes?

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QUESTION:

Problem 92GP

The fundamental of an organ pipe that is closed at one end and open at the other end is 261.6 Hz (middle C). The second harmonic of an organ pipe that is open at both ends has the same frequency. What are the lengths of these two pipes?

ANSWER:

Step 1 of 3

The following are given by the question:

The frequency,  

Speed of the sound, 

For the fundamental frequency, the length and frequency relationship is given by

                                                                       

Here,  is the length of the organ pipe closed at one end, and   is the number of harmonics.

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