PHYS 140
Interference Lab
Name:_______________________
Activity 1: Transparencies-- Interference in ripples
In this activity, you will be simulating two-source interference. Examples of this kind of interference in
real life include ripples in a pond, light emerging through 2 slits (“double slit interference”), and sound
coming from 2 speakers. We will assume that the sources are “in phase”—both “sources” of ripples will
be cresting at the same time.
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On the image below, one color represents the wave crests and the other the wave troughs. If
this was a light wave, the first color would represent electric field at its maximum strength in the
upward direction, and the color would represent
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On the transparency, using two colors as on the sheet of paper, re-draw the circle pattern by
tracing over the original pattern. Try to use similar colors as the original (one dark color and
one light / red color) so that you can match the original picture. This will produce the
interference pattern for sources that are “in phase.”
Overlap the transparency on the paper, so that the centers are slightly apart (about 3
centimeters).
Mark on the transparency all the places where opposite colors collide. Connect them to form
the lines of “destructive interference.” (They should radiate outward from the center.)
Using a protractor, estimate the angle between the center line (which is not a line of destructive
interference) and the first line of destructive interference. This is the angle that appears in the
equation for destructive interference: d sin() = (m + ½) , where m = 0 for the first line.
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Measure d. Include units.
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Calculate the wavelength using your measurements of d and 
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Does this match your actual wavelength?
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Predict what will happen to the angles between the lines of destructive interference if you
decrease the separation between the centers of the circles. (Hint: Look at the equation for
destructive interference.)
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Test your prediction by sliding the transparency in such a way that the separation decreases.
Were you correct?
Check with the instructor before continuing. Once you’re checked off, please clean off your
transparencies using rubbing alcohol.
Activity 2: Phet simulation
Another Phet simulation! Go to the Phet homepage and open the “Sound” simulation in the “Sound &
Waves” category. Select the “2 Source interference” tab. This sim is nice because you can move the
person around to detect areas of constructive or destructive interference.
1. Destructive interference.
Move the person so that his ears are sitting in an area of destructive interference. (If you enable the
audio, you’ll be able to hear when this happens—the sound will be very quiet.)
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What color (black, white, or gray) represents a “pressure node”—a place where there is no
deviation from normal pressure?
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Slide the frequency dial to 250 Hz. How many lines of destructive interference are there?
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Predict how the wavelength of the waves will change if you move the frequency to 500 Hz.
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Predict the new number of lines of destructive interference that will appear.
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Change the frequency to 500 Hz. How many destructive interference lines do you see? Were
your predictions correct?
1. Constructive Interference
Recall that constructive interference occurs when the crests of two waves align. If the waves
have the same amplitude, the amplitude of the resulting wave will be double that of a single
wave.
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The sound intensity (I) of a wave is proportional to the square of the amplitude of a wave. For
example, if you triple the amplitude of a wave, its intensity increases by a factor of 9. In your
Phet simulation, how much higher is the sound intensity of the total wave in areas where
constructive interference occurs compared to the intensity of just a single wave?
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How many decibels higher will this area of constructive interference sound compared to a single
wave? Show your calculation.
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Given that going up 10 dB is approximately a doubling of perceived “loudness,” would you
predict that the total wave in the constructively-interfering area is at least twice as loud as for a
single wave?
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Test your prediction by moving the guy from an area where he hears just the single wave to an
area where there is constructive interference. What happens to the loudness level? Is it
consistent with what you predicted?
Phet Sim #2: Double-slit interference
Open the simulation called “Wave Interference” and click the “Sound” tab. (There should be three
tabs—water, sound and light.) This simulation is interesting because it shows a different way to produce
interference. Select the “two speaker” option.
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Using the “add detector” button, sketch two graphs of pressure vs. time.
(a) Graph for a region of constructive interference
(b) Graph for a region of destructive interference
Click the “light” tab—this next measurement is easier to do with light than with sound, although the
physics works the same way. Click “Show Screen.” This is a simulation of what would happen if you
held a screen up to a double light source. Move the slit-separation slider to 1750 nm. Turn the
frequency up (blue or green is a good choice) and dial up the amplitude.
Once you have a nice pattern of colored stripes on the “screen,” you can see if your interference
pattern obeys the equation for constructive interference, by following the instructions on the next page.
First, we’ll calculate the angle between the center bright fringe and the next bright fringe. The center
corresponds to m = 0; the next bright fringe is m = 1. Unfortunately, the simulation doesn’t provide a
protractor, but you can measure the angle indirectly using trigonometry. Recall that the sine of an angle
is defined to be opposite divided by hypotenuse.
In the diagram to the right, you can see how to make a “right triangle:”
Using the “measuring tape” provided by the sim, measure the
hypotenuse of the triangle and the side “opposite” to the angle.
You can find the angle by using the inverse sine function on your
calculator (also called “arcsin”). What angle do you find? Make sure to
specify whether it’s in radians or degrees. Your calculator may either be in radian (RAD) or degree (DEG)
mode.
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Now that you have the angle, predict what the wavelength of the wave must be, using the
constructive interference formula. (Be careful about your units—keep track of whether you’re
using nm or what. A nanometer (nm) is 10-9 meters.) Show your calculation.
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Measure the actual wavelength. Is it close to what you predicted?
Check with the instructor before closing the sim and continuing.
Activity 3: Speakers
If speakers were point sources, they would produce an interference pattern much like the ones we’ve
been studying, which would cause there to be areas in front of the speakers where the sound waves
cancel out. This is a bad thing from an acoustics standpoint, so manufacturers of speakers try to make
the sound coming out of speakers a little more spread out, so that the interference isn’t as obvious.
Nevertheless, in practice, when you set up a pair of speakers, you can sometimes detect the destructive
interference.
I’ve set up a pair of small speakers in the classroom, placed one meter apart. If you walk in front of
them, it’s possible to hear a slight interference pattern (it’s subtle, not at all like the Phet simulation,
which is much more dramatic.)
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If the speed of sound is about 340 m/s and the frequency of the sources are 350 Hz, find the
wavelength of this wave. Include units.
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Prediction #1
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In class we derived that “lines” of destructive interference occur at multiple angles, given by the
equation d sin() = (m + ½) , where ‘d’ is the distance between the sources, ‘m’ is 0, 1, 2, 3,
etc., and is the wavelength. Given that the speakers are about a meter apart, predict at what
angle you will find the first (m = 0) line of destructive interference. (Express the angle in
degrees—if your calculator is in radian mode (RAD), change it to DEG. If you are using Google as
your calculator, it will give you an answer in radians unless you write “in degrees” after your
expression.)
Prediction #2
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What would you have to do to the wavelength of the sound wave to produce destructive
interference at smaller angles?
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Suppose you change your sound wave to have a frequency of 500 Hz. Find the new wavelength
and predict the angle at which you would first hear destructive interference.
Test your predictions. The speakers are powered by a function generator. Set the generator to 350 Hz.
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Walk in front of the speakers (as far back as possible), holding on to a long string so that you can
measure the angle. (Make sure you are aiming one ear at the speakers--don’t face them!). Stop
when you find an area of destructive interference. Measure the angle (the protractor should be
in the middle, between the speakers).
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Check whether a similar lessening of volume appears on the other side of the center line. Can
you hear it on the left side, the right side, or both? [In theory one ought to be able to hear it on
either side.]
Repeat the experiment for the larger frequency. What do you observe? Was your prediction correct?
Activity 4: Laser
Eye Damage Warning: When the laser is turned on, do not stick your face in front of it. To check if it is
on, put your hand in front of the laser.
A laser has been set up with a barrier (slit mask) in front of it. The barrier has sets of double slits. Turn
on the laser. It should be positioned so that the beam hits one of the sets of slits; if not, adjust it. A
meterstick is mounted a good distance away from the slits. You’ll see a pattern of fringes on the
meterstick. In fact, you should see two patterns—a large pattern with a really bright region in the
middle, and within each bright blob there is a second, smaller pattern of tiny stripes. This is because
there are two things going on here:
(1) Double Slit Interference
The light is reaching the target from two different sources
(2) Diffraction
The light waves are interfering because the width of the slits allows them to reach the target
from different angles
Which is responsible for the tinier pattern (the little stripes within each bright region)? If you aren’t
sure, here’s how you can figure it out:
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Which do you think is bigger, the width of each slit, or d (the distance between the slits)? (If you
are going to look at the mask to find out, first turn the laser OFF before sticking your head near
the slit mask!)
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Let’s look at the equation for constructive interference: d sin = m.
Given that everything on the right hand side of the equation is constant, would a small angle
(small A) correspond to a large d, or a small d?
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Use your answers above to determine whether interference or diffraction is causing the small
angle pattern. Check your answer with the instructor before continuing.
In this experiment you need to be measuring the interference pattern, not the diffraction pattern.
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The wavelength of red light is
approximately 700 nm. What is this in
meters?
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Calculate sin(A) using the definition of sine
[sine = opp/hypotenuse].
How to measure the opposite side of the triangle: Look at the tiny bright fringes. Measure the
distance between the one in the center of the big bright blob and the next one over.
How to measure the hypotenuse:
The adjacent side of the triangle is easier to measure in this set-up than the hypotenuse, but
fortunately, for very small angles, the hypotenuse is about the same length as the adjacent side.
Measure the adjacent side using a meterstick and call it the hypotenuse.
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Check that both your answers above are in the same units—if one is in meters, the other one
should be converted to meters. The units must be consistent. What is sin(A)?
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Use the equation for constructive interference to deduce the value of d for your slits.
Turn off the laser.
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Check your answer for d by looking at the values on the slit mask (where it says “spacing”—look
at the value that corresponds to the slits you were aiming the laser at). Record the actual values
below. Were they close to your measured values?
When you’ve finished this worksheet, check off your work with the instructor. Don’t leave until
your transparencies have been cleaned and put away. Thanks!