Resource Lesson
Resonance in Pipes
Printer Friendly Version
Every object, substance, has a
natural frequency
at which it is "willing" to vibrate. When an external agent applies a
forced vibration
that matches this natural frequency, the object begins to vibrate with ever increasing amplitude, or
resonate
.
For a swing, that natural frequency depends on its length, T = 2π√(L/g). If the swing is pushed at a frequency which either matches the swing's natural frequency or is a sub-multiple of that natural frequency, then the swing's amplitude builds, and we say that it is in resonance.
When air is blown across the top of a soda bottle, standing waves are set up in the air column inside the bottle and the bottle "sings."
When two identical tuning forks are placed side by side, the vibrations of one fork can force the second fork to begin to vibrate or resonate.
Image courtesy of
Clemson University, Department of Physics and Astronomy
Open-Open Pipes
Pipes can either be open on both ends or on only one end. The open ends act as free-end reflectors (producing antinodes) and the closed ends act as fixed-end reflectors (producing nodes). Let's start our investigation with a pipe open at both ends, for example, a
flute
.
Notice in the animation that both ends always remained open or "free" to move, that is they are antinodes. A summary of the first three harmonics for an open-open pipe are shown below.
Refer to the following information for the next seven questions.
Open-Open Pipe Waveforms
fundamental frequency
1st harmonic
f
_{o}
1st overtone
2nd harmonic
f
_{1}
= 2f
_{o}
2nd overtone
3rd harmonic
f
_{2}
= 3f
_{o}
Note that the frequency subscript matches the order of the overtone, NOT the order of the harmonic.
Given a pipe open on both ends is 1
.
0 meter long. What is the wavelength of the lowest frequency which causes it to resonate?
If the air temperature is 20ºC, what is the speed of sound in the pipe?
What is the fundamental frequency of this pipe?
In this same 1-meter pipe, what would be the frequency of the 4th harmonic if the temperature remains constant?
If the temperature remains constant but the pipe is cut in half, what would be the new frequency of the fourth harmonic?
Could the 0.5-meter pipe resonate at a frequency of 1543.5 hz?
Could the original 1-meter pipe resonate at a frequency of 1543.5 hz?
Open-Closed Pipes
Now let's examine a
thumb piano
, an instrument which is open at one end and closed at the other.
Notice in the animation that while the open end always remained "free" to move, the clamped end always remains "fixed." The free-end is an antinode while the fixed-end is a node. A summary of the first three harmonics for an open-closed vibrating system are shown below.
Observe that there are no "even harmonics" among the resonance states of this type of vibrating system. This stems from the fact that the fundamental frequency is a half-loop or ¼λ. Since every overtone represents the addition of a complete loop, which contains two half-loops, we can never add just one more half-loop. Thus, we cannot generate even harmonics.
Refer to the following information for the next four questions.
Open-Closed Waveforms
fundamental frequency
1st harmonic
f
_{o}
1st overtone
3rd harmonic
f
_{1}
= 3f
_{o}
2nd overtone
5th harmonic
f
_{2}
= 5f
_{o}
Note that the frequency subscript matches the order of the overtone, NOT the order of the harmonic.
Given a pipe open on one end and closed on the other is 1.0 meter long. What is the wavelength of the lowest frequency which causes it to resonate?
What is the lowest frequency to resonate in the pipe if the air temperature is 20ºC?
What would be the next lowest frequency to resonate in the pipe if the temperature remains constant?
What are the frequency and wavelength of the 2nd overtone, or 5th harmonic?
Related Documents
Lab:
Labs -
Directions: Constructive and Destructive Interference
Labs -
Doppler Effect: Source Moving
Labs -
Frequency of Vibrating Strings
Labs -
Inertial Mass
Labs -
Interference Shading
Labs -
Pipe Music
Labs -
Relationship Between Tension in a String and Wave Speed
Labs -
Relationship Between Tension in a String and Wave Speed Along the String
Labs -
Ripple Tank Checklists
Labs -
Ripple Tank Checklists
Labs -
Ripple Tank Sample Solutions
Labs -
Ripple Tank Student Involvement Sheet
Labs -
Simple Pendulums: Class Data
Labs -
Simple Pendulums: LabPro Data
Labs -
Speed of a Wave Along a Spring
Labs -
Speed of Sound in Air
Labs -
Speed of Sound in Copper
Labs -
Video: Law of Reflection
Labs -
Video: Law of Reflection Sample Diagram
Resource Lesson:
RL -
Barrier Waves, Bow Waves, and Shock Waves
RL -
Beats: An Example of Interference
RL -
Interference of Waves
RL -
Interference: In-phase Sound Sources
RL -
Introduction to Sound
RL -
Law of Reflection
RL -
Physical Optics - Thin Film Interference
RL -
Resonance in Strings
RL -
Ripple Tank Video Guides
RL -
SHM Equations
RL -
Simple Harmonic Motion
RL -
Sound Level Intensity
RL -
Speed of Waves Along a String
RL -
The Doppler Effect
RL -
Vibrating Systems - Simple Pendulums
RL -
Vibration Graphs
RL -
Wave Fundamentals
RL -
Waveform vs Vibration Graphs
REV -
Orbitals
Review:
REV -
Chapter 26: Sound
REV -
Honors Review: Waves and Introductory Skills
REV -
Physics I Review: Waves and Introductory Skills
REV -
Sound
REV -
Waves and Sound
REV -
Waves and Sound
Worksheet:
APP -
Echo Chamber
APP -
The Dog-Eared Page
CP -
Light Properties
CP -
Reflection
CP -
Shock Waves
CP -
Sound
CP -
Waves and Vibrations
NT -
Apparent Depth
NT -
Atmospheric Refraction
NT -
Concert
NT -
Light vs Sound Waves
NT -
Shock Cone
NT -
Sound Waves
NT -
Standing Waves
WS -
Beats
WS -
Beats, Doppler, Resonance Pipes, and Sound Intensity
WS -
Counting Vibrations and Calculating Frequency/Period
WS -
Doppler - A Challenge Problem
WS -
Doppler Effect
WS -
Fixed and Free-end Reflections
WS -
Fundamental Wave Terms
WS -
Interference: In-phase Sound Sources
WS -
More Practice with Resonance in Pipes
WS -
More Practice with the Doppler Practice
WS -
Practice with Resonance in Pipes
WS -
Practice with the Doppler Effect
WS -
Practice: Speed of a Wave Along a String
WS -
Pulse Superposition: Interference
WS -
Ripple Tank Review
WS -
Sound Vocabulary
WS -
Speed of Sound
WS -
Speed of Sound (Honors)
WS -
Standing Wave Patterns #1
WS -
Standing Wave Patterns #2
WS -
Standing Wave Patterns #3
WS -
Standing Wave Patterns #4
WS -
Vibrating Systems - Period and Frequency
WS -
Wave Phenomena Reading Guide
WS -
Wave Pulses
WS -
Waveform and Vibration Graphs #1
WS -
Waveform and Vibration Graphs #2
TB -
25A: Introduction to Waves and Vibrations
TB -
25B: Vibrations and Waves
TB -
25C: Wave Speed
TB -
25D: Interference
TB -
25E: Doppler
TB -
25F: Doppler Effect (continued)
TB -
26B: Speed of Sound
TB -
26C: Resonance
TB -
26D: Beats
TB -
26E: Decibels
TB -
27A: Light Properties
TB -
Decibels and Sound Intensity #1
TB -
Decibels and Sound Intensity #2
TB -
Interference Re-examined
TB -
Refraction Phenomena Reading Questions
TB -
Sound: Mixed Practice
TB -
Waves and Vibrations
PhysicsLAB
Copyright © 1997-2015
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton