Resonant Frequencies of a Pipe
Sound is a longitudinal (compression) wave representing pressure variations in a
medium. The frequency of a sound wave corresponds to how often regions of high
pressure (high density of molecules) occur at a certain point.
Standing sound waves in a pipe
OPEN PIPE
A pipe open at both ends is like having a string with fixed ends. This is because if the
pipe is open to the air, the pressure is “fixed” at atmospheric pressure at that point. But
the pressure can vary inside the pipe, creating a sound wave.
n=1
number of wavelength(s) in the pipe
½  =
2 L  f1 = v/ =
v/(2L) .
n=2
number of wavelength(s) in the pipe _______   = ________  f2 = v/ = _____________.
n=3
number of wavelength(s) in the pipe _______   = ________  f3 = v/ = _____________.
General pattern: fn = ___________.
PIPE WITH ONE CLOSED END AND ONE OPEN END
The open end of the pipe is a node (fixed to atmospheric pressure). At the closed end,
the pressure can vary between high pressure and low pressure.
n=1
number of wavelength(s) in the pipe _______   = ________  f1 = v/ = _____________.
n=2
number of wavelength(s) in the pipe _______   = ________  f2 = v/ = _____________.
n=3
number of wavelength(s) in the pipe _______   = ________  f3 = v/ = _____________.
General pattern: fn = ___________.
Experiment
In this experiment, we adjust the (effective) length of a pipe by raising
the water level in the bottom. A speaker at the top creates a sound
wave of a certain frequency f.
This frequency may or may not satisfy the equation f = (2n – 1)v/(4L). If
it does, you hear a loud sound (resonance).
Make a prediction (work with your neighbor)
You have a pipe of length = 1m and a speaker that puts out a sound of 330 Hz. Given the speed of sound
in air is roughly 330 m/s, how much of the pipe would you have to fill with water to hit a resonance?
Suppose I asked you to find what length of pipe you'd need to set up a standing sound
wave in a column of air. What information would you need to know?
a) The velocity of sound in air
b) The frequency of the sound wave
c) Whether the pipe was open or closed on the ends
d) all of the above
Suppose I hand you a length of pipe, closed at one end and open at the other. A sound source
that has an adjustable frequency is placed near the opening. You turn on the sound source, and
place a microphone at the open end.
1) How can you tell if the sound waves are resonating in the pipe? (ie, forming a standing wave.)
2) Suppose you turn on the source and all you hear is a quiet buzzing—no resonance. What
happens as you change the frequency of the sound source? Say you increase it a little. Then a
little more...then a lot more...what happens?
3) Suppose you find a frequency that makes the sound coming from the mike very loud. You've
made the sound wave resonate. Keeping the frequency the same, what happens if you
lengthen the pipe a little? What do you expect to happen if you continue increasing the length
of the pipe?