Instructor Outline: Resonance
UM Physics Demo Lab 07/2013
Lab length: 70 minutes
Lab objective: Instruct the students about period, frequency, amplitude, wave
velocity, resonance, simple harmonic motion (pendulum) and standing waves.
Materials
1
2
1
1
1
1
2
1
1
1
1
length of string
nuts (pendulum bobs)
ring stand
stopwatch
piston assembly
small plastic storage tub (piston support)
tuning forks – one labeled, one unknown
measuring tape
ruler
calculator
digital scale
Exploration stage: 20 minutes - Group Lab Work
The students work in groups to build pendulums. They test which variables
affect the period.
Analysis stages: 15 minutes – Lecture
Simple Harmonic Motion is presented for a mass on a spring and for the
simple pendulum. The concepts of period, frequency and amplitude are introduced
for oscillations.
Application stage: 25 minutes – Group Lab Work
The students observe resonance with resonance chambers. They calculate the
speed of sound with a known frequency tuning fork, and then calculate the frequency
of an unknown fork. The students draw upon the concepts introduced in the previous
Waves Lab, including nodes, anti-nodes, overtones and wave diagrams for standing
waves in tubes.
Summary: 10 minutes – Lecture and Demonstration
The Tacoma Narrows bridge disaster is presented and a wine glass shattered
as a final demonstration of the potential danger that exists if structures are
accidently driven at resonance.
Suggested Demos:
3A60.10 - Tacoma Narrows Video Clip
3D40.55 - Shattering the Wine Glass
3D32.10 - Organ Pipes
3C55.U1 – Helium Voice
3A40.31 – Linear Projection of Rotational Motion
-Waves on a String Apparatus from Previous Waves Lab
-Assorted Masses and springs to Demonstrate Dependency of Frequency on K and m
for a Simple Harmonic Oscillator
-Microphone and Visual Analyzer Oscilloscope program to show Fourier spectrum of
various sounds—tin whistle, train whistle, harmonica, tuning fork and organ
pipe.
Property of LS&A Physics Department Demonstration Lab
Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109
Concepts Developed:
1. Mechanical systems have natural frequencies at which they will oscillate if
disturbed.
2. Period and frequency describe the behavior in time of oscillating systems.
The relationship between the frequency f (number of oscillations/second) and
the period T (number of seconds/oscillation) is f 
1
.
T
3. Amplitude is the magnitude of the oscillation and is independent of the
frequency.
4. The natural frequency for mass-and-spring oscillator is
f 
1
2
k
where k is
m
the Hooke’s Law spring constant (Newtons/meter).
5. The natural frequency for a pendulum is
6.
7.
8.
9.
f 
1
2
g
where g is the
L
acceleration of gravity and L is the length of the pendulum. The frequency
does not depend on the mass of the pendulum bob.
The natural frequency of a mass-and-spring system does not depend on the
acceleration of gravity and will be the same everywhere in the universe.
The frequency of a pendulum depends on the acceleration of gravity and will
therefore be different on different planets. The frequency or period of a
pendulum can be used to perform sensitive measurements of the local
acceleration of gravity on Earth or any other planet.
Resonance occurs when the driving frequency of an external force applied to
an object or system matches the natural frequency of the system. The
amplitude of oscillations will grow with time if a system is driven at
resonance, since the system is absorbing more energy as it is driven.
One can measure the speed of sound with a known frequency tuning fork and
a chamber.
Property of LS&A Physics Department Demonstration Lab
Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109