The frequency of the first harmonic standing wave in a pipe that is open at both ends is 200 Hz. What is the frequency of the first harmonic in a pipe of the same length that is open at one end and closed at the other?

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wietselau · Accepted Answer

Consider that for an open pipe,      f          n        =  n  ∗      ν          2      ℓ      Given,      f          1        =  200  H  zHence the length that the pipes share is,  ℓ  =      ν          2              f                  1                      ≈  85.8  c  mNow, consider that for closed pipes,      f          n        =  n  ∗      ν          4      ℓ      A node must be at the closed end and an antinode at the open end to let sound waves propagate. Thus, for every             n      λ        4  , (where n = odd), the waveform is in this orientation.Hence, the fundamental frequency of a closed pipe of the same length is,      f          1        =      ν          4      ℓ        ≈  100  H  z

The frequency of the first harmonic standing wave in a pipe that is open at both ends is 200 Hz. What is the frequency of the first harmonic in a pipe of the same length that is open at one end and closed at the other?

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