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?

The answer is 100 Hz. Is it because the frequency is half in first harmonic wave motion.

1 Answer
Al E.
May 1, 2018

Consider that for an open pipe,

#f_n = n * nu/(2ℓ)#

Given,

#f_1 = 200"Hz"#

Hence the length that the pipes share is,

#ℓ = nu/(2f_1) approx 85.8"cm"#

Now, consider that for closed pipes,

#f_n = n * nu/(4ℓ)#

A node must be at the closed end and an antinode at the open end to let sound waves propagate. Thus, for every #(nlambda)/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 = nu/(4ℓ) approx 100"Hz"#

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