Instructor Outline: Waves
UM Physics Demo Lab 07/2013
Lab length: 70 minutes
Lab objective: To instruct the students about traveling waves, propagation speed on
a string, the relationship between frequency, wavelength and speed for a traveling
wave, standing waves, nodes, antinodes and overtones.
Materials
1
1
1
2
wave-motor apparatus
battery board
card alligator leads
squeeze clamps
Exploration stage: 30 minutes - Group Lab Work
The students observe standing waves. They test which variables contribute to
the number of nodes and antinodes.
Analysis stages: 20 minutes – Lecture
Traveling waves are introduced, both longitudinal and transverse. Next the
propagation speed on a string as related to the tension and linear mass density for
the string are introduced. The relationship between propagation speed, frequency
and wavelength is then introduced. Standing waves are discussed with an
introduction to the concepts of nodes and antinodes.
Application stage: 20 minutes – Group Lab Work
The students fill out overtone diagrams for open and closed tubes with forced
nodes and anti-nodes. This builds an understanding of overtones.
Suggested Demos:
3B22.u1 - Rubens Flame Tube
Longitudinal and Transverse Waves Propagated on a Slinky
Concepts developed:
1. Traveling waves are a disturbance in a medium that propagates energy from
one place to another.
2. The elastic medium oscillates about its equilibrium position as the traveling
wave passes but does not travel from one place to another with the wave.
3. The speed of propagation for an elastic wave depends only on the properties
of the medium, not on the amplitude, frequency or wavelength of the wave.
4. The distance between two successive wave crests is called the wavelength
and is denoted by the Greek letter λ. The units of wavelength are meters.
5. The number of wave crests passing a fixed point per second is called the
frequency of the wave and is denoted as f. The units for frequency are
cycles/second denoted as Hertz (Hz).
6. The amplitude of a wave is the maximum excursion from equilibrium in the
medium as the wave propagates. The amplitude is independent of frequency
or wavelength.
7. The fundamental relationship governing all traveling waves is v  f  where v
is the propagation speed of the wave, f the frequency and λ the wavelength of
the wave. Changing f or λ does not change the propagation speed.
Property of LS&A Physics Department Demonstration Lab
Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109
8. For waves on a string the propagation speed is
v
T
where T is the
m
L
tension force applied to the string and m/L the mass per unit length of the
string.
9. Standing waves occur on a string when both ends of the string are fixed and
the string is made to vibrate.
10. Nodes are positions along the standing wave where the amplitude of the
oscillation is zero at all times.
11. Antinodes are positions along a vibrating string where the amplitude of the
oscillation is a maximum at all times.
12. For sound standing waves in a tube, a closed end of the tube is forced to be
a node.
13. For sound standing waves in a tube an open end of the tube is forced to be
an antinode.
14. The lowest frequency standing wave that can exist on a string or in an
acoustic tube is called the fundamental frequency.
15. Higher frequency standing waves which can also exist on a vibrating string or
in an acoustic tube are called overtones.
Property of LS&A Physics Department Demonstration Lab
Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109