Enter the frequency, speed of sound, and length of the pipe into the calculator to determine the missing variable for closed pipe resonance.
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Closed Pipe Resonance Formula
The following formula is used to calculate the resonance frequency, speed of sound, or length of the pipe for a closed pipe resonance.
f = \frac{v}{4L}Variables:
- f is the frequency in hertz (Hz)
- v is the speed of sound in meters per second (m/s)
- L is the length of the pipe in meters (m)
To calculate the resonance frequency, divide the speed of sound by four times the length of the pipe. This formula can also be rearranged to solve for the speed of sound or the length of the pipe.
What is Closed Pipe Resonance?
Closed pipe resonance occurs in a pipe that is closed at one end and open at the other. The closed end acts as a node where the air particles do not move, while the open end acts as an antinode where the air particles move with maximum amplitude. This setup creates a standing wave pattern within the pipe, with the fundamental frequency determined by the length of the pipe and the speed of sound in the medium. Closed pipe resonance is commonly observed in musical instruments like organ pipes and some wind instruments.
How to Calculate Closed Pipe Resonance?
The following steps outline how to calculate the closed pipe resonance.
- First, determine the speed of sound in the medium (v).
- Next, measure the length of the pipe (L).
- Finally, calculate the resonance frequency using the formula f = v / (4L).
- If you have the frequency and length, you can rearrange the formula to solve for the speed of sound.
- After inserting the values and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Speed of sound (v) = 343 m/s
Length of the pipe (L) = 0.25 m