An open organ pipe has a fundamental frequency of 240 vib / s. The first overtone of a closed or

step 1 In the question it is given an open organ pipe has a fundamental frequency of 240 vibrations per

An open organ pipe has a fundamental frequency of 240 vib /...

An open organ pipe has a fundamental frequency of $240 \mathrm{vib} / \mathrm{s}$. The first overtone of a closed organ pipe has the same frequency as the first overtone of the open pipe. How long is each pipe? Velocity of sound at the room temperature is $350 \mathrm{~ms}$.

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Key Concepts

Fundamental Frequency and Pipe Length Relationship

This concept explains that the frequency at which a pipe resonates is directly related to its length and the speed of sound. For an open pipe, the fundamental frequency is given by f = v/(2L), and for a closed pipe, it is f = v/(4L). Understanding this relationship allows one to calculate the length of the pipe when the fundamental frequency and the speed of sound are known.

Open versus Closed Pipe Boundary Conditions

Open and closed pipes differ in their boundary conditions. In an open pipe, both ends are open resulting in antinodes at each end. Closed pipes have one open end and one closed end, leading to an antinode at the open end and a node at the closed end. This difference affects the harmonic series that each pipe can support.

Harmonic Series and Overtones

The harmonic series refers to the set of frequencies at which a system resonates. In an open pipe, harmonics occur at integer multiples of the fundamental frequency, while in a closed pipe, only the odd multiples appear. This concept is crucial for understanding how overtones (the additional frequencies above the fundamental) are produced in each type of pipe.

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