The fundamental frequency of a pipe that is open at both ends is 594 Hz .How...

Question

The fundamental frequency of a pipe that is open at both ends is 594 Hz .

How long is this pipe?

If one end is now closed, find the wavelength of the newfundamental.

If one end is now closed, find the frequency of the newfundamental. [su_box title="♦ Relevant knowledge" box_color="#2d6ff7" radius="1"]Strings and pipes used on musical instruments all contain fundamental frequencies. It will be the lowest-frequency that is able to be accommodated onto the string or the pipe. The fundamental frequency is determined by how long the pipe or string and whether the edges of the pipes are open, or closed. Pipes and strings also possess harmonics with higher frequency that's more than that of fundamental. With harmonics and the fundamental instruments with a restricted amount of pipes or strings can produce a broad range of tones.

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Connor Wang · Accepted Answer

Concepts and Reason

This problem was solved by using open and closed endpipe harmonics.

To determine the length of a pipe, use the fundamental frequency of an open pipe at both ends.

Next, use the length of the pipe to determine the wavelength of the fundamental frequency and the fundamental frequency for a one-end closed pipe.

Fundamentals

The fundamental frequency of a pipe with both ends open is expressed as,

f₀ refers to the fundamental frequency of a pipe with both ends open, v the velocity of sound and L the length of the pipe.

The fundamental frequency of a pipe, which is only one-end closed, is expressed as

f refers to the fundamental frequency of a pipe with both ends open, v the velocity of sound and L the length of the pipe.

The wavelength of the fundamental of a closed one-end pipe is expressed as,

λ here is the wavelength for fundamental.

(1) The fundamental frequency of a pipe with both ends open is expressed as,

Adjust the expression above to adjust the length of your pipe.

The length of the pipe will therefore be 0.290 m.

(2) The wavelength of the fundamental of a closed one-end pipe is expressed as,

Modify the expression above for λ.

The wavelength of the fundamental of a one-end closed pipe is 1.16 m.

(3) The fundamental frequency of a pipe, which is only one-end closed, is expressed as

The fundamental frequency of a pipe with one end closed is 297 Hz.

Ans:

Part 1: The length of the pipe measures 0.290 m.

Part 2: 1.16 m is the wavelength of the fundamental of a closed one-end pipe.

Part 3: The fundamental frequency for a pipe that is not closed at one end of the line is 297 Hz.

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