University of Puget Sound Introductory Physics Laboratory
1. Waves in one dimension
Name:____________________
Date:___________________
Objectives
1. To investigate the nature of traveling and standing waves.
2. To determine experimentally the relationship between wave speed, wavelength,
and period for periodic waves.
3. To re-familiarize yourself with some of the experimental principles and methods
that you learned last term.
Equipment
Long springs, stopwatch, function generator, driver coil and tensioned string.
Introduction
A wave is a traveling disturbance. A wave can transfer energy from one place to
another without transferring matter. Waves can be either pulsed or continuous. For
example, imagine you are holding onto one end of a taut rope and then quickly move
your hand back and forth. You create a single disturbance - a pulse - that moves down
the rope. If you rhythmically move your hand back and forth you can create a periodic
train of wave pulses on the rope. For waves traveling on a taut rope both of these kinds
of disturbances move at the same speed, determined by the conditions of the rope. In
general, the kinds of disturbances you can create come in two flavors: transverse and
longitudinal. For a transverse wave, the disturbance is perpendicular to the direction of
energy transfer (for example, light is a transverse wave). For a longitudinal wave, the
disturbance is in the same direction as the direction of energy transfer (for example,
sound is a longitudinal wave). In this lab you will create both transverse and
longitudinal waves on stretched springs, and take measurements to investigate the
relationship between wavelength, period, and wave speed for standing waves on a
rope.
Spring experiments
Get a long coil spring and find a spot to work in the hallway. Stretch the spring
out a bit, but not so far as to deform it permanently. Generate a wave pulse with your
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hand. Can you make pulses of different shapes? To make a good pulse, try the
following set-up:
hand
hand
partner
foot
Try making a longitudinal wave too. Do they move at the same speed? Can you make
pulses that are always on one side or the other of the centerline of the spring? Can you
make one that straddles both sides? How? Answer the above questions and draw a
few of your pulsed waves in the box below.
Note the length of the spring (you can use the tile squares for a measuring stick.
They are 9" or 3/4' wide). Estimate the speed of your wave pulse by making time
measurements using a stopwatch. Vary the length of the spring over as wide a range as
possible (what principle is this?). For each length, repeat your speed measurement, say
6 times. It's not easy to make the time measurement. Practice a bit to improve your
technique. In the space below, put your data in the table, and create a graph of wave
speed versus the length of the spring. Use a straight edge to draw your axes. Label and
scale your axes, and give your graph a descriptive title. Put error bars on your data
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points using the quick and dirty statistics method that we used last term (see the
appendix if need be).
trial
trial trial trial trial trial
uncertainty
spring
1
2
3
4
5
6
average in average
length
time time time time time time time
time
(meters) (secs)
(secs)
(secs)
average
wave
speed
(m/s)
uncertainty
in average
speed
(m/s)
Describe what your graph is telling you.
If you throw two baseballs at each other you get a collision. What do you get
when you throw two waves at each other? Two wave pulses on your spring exhibit
interference. That is, at any spot on the spring the total deflection away from the
centerline should be the sum of the deflections from the two wave pulses. Try sending
pulses from each end of your spring and examine the deflection of the spring in the
region where the pulses pass each other. It's hard to see because the pulses move pretty
quickly. What can you do to slow the pulses down? Do it. Can you see the
interference now? Probably not. You could try viewing the spring through a slot in a
piece of cardboard, so your eyes would only observe the spring in a narrow region. Try
that. There's another fun way to do it. Set up a row of styrofoam cups adjacent to the
spring, close enough to the spring so that a single wave pulse would knock them over.
Try sending two pulses at each other and see if the cup in the interference region gets
knocked over. In the space below, draw a sequence of a half a dozen or so pictures
showing how the pulses approach each other, interfere, and continue past each other.
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Standing wave experiments
With your spring, generate a continuous wave by rhythmically moving your
hand back and forth. Vary the rate that you jiggle the end of the spring until you get a
nice standing wave oscillating back and forth. Try to increase the amplitude (without
changing the rate of jiggling). Does it feel like you are doing more work on the spring?
You bet. You can think of what's happening as an energy transfer process: the work
you do ends up as energy stored in the spring. Now increase the rate at which you
jiggle the end of the spring. Can you make one, two, three, four bumps in your
standing wave pattern? The time for your hand to move back and forth is called the
period; the inverse of the period is called the frequency and is measured in Hertz (or
cycles per second). The wavelength is the distance over which the pattern repeats, in this
case two bumps (why not one bump?). There's clearly a relationship between the
driving frequency and the wavelength. What is the wavelength for each of the standing
waves that you were able to generate? Should the wave speed be the same for all of
these waves? How do you know?
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There's a general relationship between wave speed, wavelength, and period for
periodic waves. It's easy to remember: the wave moves one whole wavelength in a
period. In this last experiment, I want you to see if it really works that way. It's hard to
control and measure the frequency of your spring waves, so instead of your hand we'll
use an electrical generator that drives a mechanical vibrator. An elastic string is jiggled
by a vibrator on one end and attached to a mass hanging over a pulley on the other end
(this sets the tension, and hence the wave speed). On your "function generator" there
are two knobs: frequency and amplitude. One controls how fast the vibrator vibrates,
the other controls the size of the vibrations. Turn the generator on, set the amplitude
for midrange, and twiddle the frequency knob. Scan around in frequency and look for
large amplitude standing wave modes. If you jiggle the string at one of its "natural"
frequencies, it will suck up energy from the vibrator and show large oscillations. This is
called resonance. You are hunting for the resonant frequencies of the stretched string.
Try touching the string at a node (a stationary point). Touch it at an anti-node. What
happens? How can you explain that there are nodes if you think of the disturbance as
waves propagating down the string?
The large amplitude resonant frequencies should approximately be multiples of
the lowest resonant frequency. Check this out. Once you get comfortable tuning the
string to any of the resonant frequencies, measure these frequencies and put them in the
table below, along with the wavelength for each resonant mode. How many modes can
you create (8? 10?)? Double the mass hanging off of the string and repeat your
measurements. Draw a set of axes below, label and scale them, and plot wavelength
versus period (the inverse of frequency) for both of your data sets. What do you expect
your data to look like? Draw a smooth curve corresponding to your expectations
through your data (A straight line? A curved line? Does it go through the origin?).
From your graphs determine the wave speed for both values of the rope tension.
Estimate the uncertainty in these speeds crudely by considering the variation in the
slope of a line that runs through the data points.
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trial 1: hanging mass = _______________
frequency
(Hz)
period
(sec)
trial 2: hanging mass = _______________
wavelength
(centimeters)
frequency
(Hz)
period
(sec)
wavelength
(centimeters)
What you need to do to escape: check in with your lab instructor, and
(1)
explain what determines the wave speed on a stretched spring, and provide
experimental evidence for your claim.
(2) show the instructor your graphs for wavelength versus period from your last
experiment. Argue why your measured wave speeds and their uncertainties are
physically reasonable in magnitude.
(3) compare the dependence of wave speed on spring tension for your last experiment
with your first experiment (timing the pulse transit). Are they consistent? Make an
argument concerning the dependence of wave speed on tension.
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