University of Puget Sound Introductory Physics Laboratory
2. Waves in two dimensions
Name:____________________
Date:___________________
Objectives
1. To observe the reflection of waves from various obstacles, and to become
familiar with the concept of imaging.
2. To observe the phenomena of refraction and diffraction, and to investigate
the nature of their dependence on wavelength and frequency.
Equipment
Ripple tanks with oscillating drivers and various obstacles, and a hand strobe.
Introduction
In today's lab exercises, you will observe a variety of different wave
phenomena. In later labs we will be studying light, which exhibits many of the
same wave effects. We start by studying water waves because they are visible
with wavelengths that are macroscopic, and hence, unlike light, we can see the
"waving" occur.
Water waves are two dimensional, that is, the wave moves around in a
two-dimensional space (even though the water molecules move in three
dimensions). The wave amplitude is just the height of the water measured from
the level of the undisturbed water surface. Unlike the waves on the string that
you studied in the last lab, the speed of the water wave depends on the
wavelength. This is called dispersion. Physicists say things like "the waves on a
taut rope are dispersionless" and "a prism disperses white light according to
color (wavelength)". We won't have to worry about this effect today because
you will be creating waves that are nearly sinusoidal, and hence are periodic
with a unique wavelength and wave speed. We will take up dispersion later
when we begin our studies of light.
Procedure
Before you is a ripple tank on the tabletop with white paper under the
legs. A light source should be located about the same distance above the tank as
the paper is below it. If it isn't already, fill the tank with water to a depth of 6 to
8 mm. Check to make sure that the tank is leveled so that it has equal depth all
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the way around. Gently touch the water surface with your fingertip or with the
point of a pencil, and observe the image of the wave that this creates on the
paper below. How does the wave travel in the water compared with the way the
water itself moves? Can you assign a direction to the wave at any point? How
does the velocity of the water wave relate to the velocity of its image on the
paper? Use the box below to answer the above questions.
Reflections from Barriers
Place a wooden dowel along one edge of the tank and gently roll it back
and forth a fraction of an inch. This should create a "plane wave," with parallel
wave fronts propagating across the tank. Set up the vibrator to jiggle your dowel
for you, and adjust the frequency of the vibrator so that the wavelength is good
for viewing. You can use this continuously generated plane wave to investigate
the interaction of waves with obstacles. Lay a thick, straight edged barrier in the
tank and send your plane waves into the barrier. The barrier should be tall
enough so that there's no water on top of it and all of the wave will be reflected.
Try this out for plane waves coming into the barrier at three different angles. On
the paper under the tank sketch the shadow of the barrier, the incoming and
reflected wavefronts (a snapshot in time), and also the normals to the
wavefronts. From your drawing, measure the incoming and reflected angles in
your three cases, and convince yourself that the wavefronts bounce off of the
barrier like billiard balls (angle of incidence equals angle of reflection, measured
from the normal to the barrier). In the space below, sketch your set-up for one
angle of incidence, list your measured angles of incidence and reflection, and
comment on their agreement (or disagreement) in light of your measurement
uncertainty.
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The light bouncing off your nose goes in all directions, not just in one
direction like a plane wave. So let's study the reflection of circular pulses from a
straight barrier. You can use the vibrator with a single ball attachment to create
circular wavefronts. Observe the shape of the wavefronts reflected from a
straight barrier. Stare at the reflected waves and try to ignore the incoming
waves and the barrier. Do the reflected waves look like they are originating from
somewhere? Find this spot. This is the image of the point of vibration in the
barrier. We call this a virtual image, since there's nothing real (no wave) at its
location. Carefully draw a picture of this set-up below. If you move the vibrator
around, where does the image go? This works just like light bouncing off of a
flat mirror. If you walk around in a room with one mirrored wall, where does
the image of your nose go? Why should your image in a mirror behave the same
way as water waves bouncing off a barrier? Hmm.
for questions
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for sketches
Curved mirrors focus light. Try reflecting plane waves from a curved
barrier, using rubber tubing or a strip of metal for the barrier. What happens to a
plane wave incident on the concave (curved inwards) side of the barrier? Find
the point where the reflected waves converge. This is called the focal point. Start
a circular pulse with your finger at the focal point, and observe the shape and
direction of the wave reflected by the barrier. Cool! The movie plays backwards.
Now try bouncing a plane wave off of the convex (curved outwards) side of the
barrier. Where do the reflected waves appear to converge? Is there anything
there? Draw a picture of both cases below; identify in each case the location of
the focal point.
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Refraction from a Partial Barrier
When you look at a straw in a glass of water, the image of the straw looks
bent. The light from the straw that reaches your eyes goes from one medium
(water) to another (air). It turns out that the speed of light is slower in water
than in air, and this can explain the bending of the light. You can investigate this
phenomenon in your water tank. Form a partial barrier in the tank by
submerging a plastic plate (or plates), so that the plate is just covered with water.
This creates an abrupt change in the depth of the water. The speed of water
waves in shallow water depends on the depth, so a wave crossing this barrier
will be forced to change speed. This speed change causes a direction change,
which is referred to as refraction. (If you are interested, get your instructor to tell
you a story about soldiers marching in formation from land into knee-high
water....)
Set the vibrator up for making plane waves at a frequency that is
convenient for observing the wavelength and wave speed. Observe the
refraction of the plane waves at three different angles of incidence to the partial
barrier. Sketch the incident and refracted wavefronts on the paper in each case.
Measure the incoming and refracted angles in each case. Do you observe a
general trend in the bending of the wavefronts as you vary the angle of
incidence?
Using a hand strobe, "stop" the waves in the deeper water. Are the waves
in the shallower water also stopped? What does this say about the frequency of
the waves in the two media? Is the wavelength in the shallower water the same
as the wavelength in the deeper water? Larger or smaller? Think about last
week's lab. Is the wave speed in the shallower water faster or slower than the
wave speed in the deeper water?
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Something else to try if you are curious: tilt the tank just a little bit, so that
the depth of the water varies across the tank. Don't get wet. This is like a good
surfing beach, or a material with a graded index of refraction (like a fiber optic
cable). Set up a plane wave in the deep water, and see how the wave travels into
the shallow water. Can you observe a change in wave speed across the tank?
How? Try it with different angles of incidence with respect to the "beach." Can
you relate this to light phenomena, such as the appearance of mirages and the
apparent position above the horizon of the setting sun?
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Diffraction from Obstacles and Apertures
Light streaming through a doorway makes a crisp shadow. The spreading
of a wave into a "shadow" area can be observed when a wave encounters an
obstacle whose size is comparable to the wavelength of the wave. This wave
spreading is called diffraction. You can easily observe diffraction in your wave
tank. Set the vibrator to make plane waves of long wavelength, and place a
small block in the tank a few inches from the plane wave generator. Does the
block cast a crisp shadow? Do the waves continue in their straight-line path on
both sides of the block? Can you sense the presence of the block by looking at
the wave pattern at the far end of the tank? Try varying the block size, and
describe the effect of block size on the shadow pattern.
Try repeating the above experiment for an aperture instead of an obstacle.
You can make an aperture using two blocks with a gap between them. Observe
the behavior of the waves as they emerge from the aperture. Are long
wavelength waves still straight beyond the aperture? Do the waves travel in the
original direction? Leave the gap size fixed, vary the wavelength of the water
waves. Sketch what happens to the diffraction pattern as you decrease the
wavelength. Now vary the width of the aperture and observe the pattern
change. In terms of ratio of the aperture size d and the wavelength , under
what conditions do you observe diffraction effects?
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Before you leave:
Show your instructor your work.
Explain to your instructor where your image appears in a mirror. Go to the
blackboard and draw a diagram of you, a mirror, and your image.
Describe the criterion that you deduced for when you would expect to see
diffraction effects.
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