12. PRELAB FOR INTERFERENCE
LAB
1.
INTRODUCTION
As you have seen in your studies of standing waves, a wave and its reflection can
add together “constructively” (peak meets peak, giving large amplitude) or
“destructively” (peak meets valley, canceling each other). This type of adding is called
INTERFERENCE, and it depends on the relative phase of the interfering waves. Since
the direct and reflected waves are coming from the same source, they clearly start out in
phase. Whether or not they come back together in phase depends on path length. If the
difference in the two path lengths is 1,2,3,etc. wavelengths, then the waves will be back
in phase. If there is an extra ½ wavelength, however, they will be out of phase.
2. AN EXAMPLE OF MICROPHONE PLACEMENT
The next page contains an excerpt from an article on the importance of a
microphone placement. Read the excerpt and answer the following questions:
1.
When the pressure wave is reflected from the table, is there a 180o phase shift?
(Think back to the standing waves in the open and closed tubes).
2.
Look at Fig. 4.10 from the excerpt. Suppose that the direct sound travels 2
meters, and the reflected sound covers a greater distance of 2 ½ meters. Therefore, the
difference in the two path lengths is d = 0.5m. Constructive interference will occur when
d = λ, 2λ, 3λ, 4λ, … , where λ is the wavelength. Use the relation v = λ f, (v – speed of
sound, f – frequency) to calculate the first four frequencies at which constructive
interference will occur. Assume v = 344 m/s. Then, calculate the first four frequencies at
which destructive interference (d = ½ λ, (1+½) λ, (2+½)λ , …) will occur.
Constructive interference
Destructive interference
1.
f1 (constr) =
Hz
f 1(destruct) =
Hz
2.
f2 (constr) =
Hz
f 2(destruct) =
Hz
3.
f3 (constr) =
Hz
f 3(destruct) =
Hz
4.
f4(constr) =
Hz
f 4(destruct) =
Hz
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3.
INTERFERENCE PATTERNS IN SPACE
Pressure pulses travel out from a sound source in concentric spheres. When two
closely spaced, identical sources emit sounds, an interference pattern of loud and soft is
produced.
1.
The next page shows such an interference pattern. The lines drawn through the
crossing points of the circles show the loud areas.
2.
The page after that is blank. Use a COMPASS to make an interference pattern
like the example, except with the sources closer together, as shown. The scale at the
bottom of the the page shows the spacing of the circles of high pressure. Draw lines
through the crossing points to show the loud regions. Mark with dotted lines the soft
regions.
3.
Use another blank page to make a drawing assuming the same source separation
as before, and twice longer wavelength.
4.
Compare cases 1, 2 and 3. Write down your observations.
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An example of interference pattern
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Prelab assignment: Draw an interference pattern for the given speakers
separation and the same wavelength as on previous page. Either use the same drawing ,
or a separate blank page to see the effect of doubling the wavelength.
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12A. INTERFERENCE LAB ACTIVITIES
0. DEMONSTRATIONS
We will start this lab with two demonstrations illustrating your prelab analysis.
1.
a.
Interference and microphone placement demonstration.
b.
Water waves in a Ripple tank.
STANDING IN A RIPPLE TANK OF SOUND
This is an outdoor activity. Two loudspeakers will be mounted in the room
windows pointing toward the 3rd Street. They will be driven by a Function generator set
to a sine wave of 400 Hz. This frequency, coupled with the speed of sound of 344 m/s
corresponds to the sound wavelength of λ = 344 m/s / 400 Hz = 0.86m. The speakers
will be approximately 1.2m apart. The sound from the two speakers will form an
interference pattern analogous to the one discussed in your prelab and shown for water
waves. To observe this pattern the students will assemble on the sidewalk outside the
building. They are asked to walk back and forth along the sidewalk finding the loud and
soft places.
1.1 Straight Lines with Maximum or Minimum Sound
Find the position of central maximum. Students should form a line going out
toward 3rd Street along the central maximum, as shown in the figure.
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Next, each student should walk East, until he/she finds the first minimum of
sound. Stop there. The students should again be forming a straight line pointing to the
place between the two speakers. If you continue, you should find the first secondary
maximum. Again, students are expected to form a straight line pointing at the center.
Find positions of at least the first TWO minima and ONE secondary maximum. Repeat the
measurements walking West from the central maximum. Positions of minima and maxima either
to the East or to the West are expected to be symmetric with respect to the central axis.
1.2
Data recording
Using a measuring tape, find (one measurement for all students):
-
separation between speakers, D =
-
distance from the building to the far edge of the sidewalk, L =
-
positions of minima along the far edge of the sidewalk, with respect to the
, dmin2 =
central maximum: dmin1 =
-
1.3
position of the secondary maximum along the far edge of the sidewalk,
with respect to the central maximum: dmax1 =
Data analysis (to be completed once you are back in the building).
Using the measured values of D and L and the known wavelength λ = 0.86 m, predict
values of dmin 1, dmin 2, and dmax 1 .
There are two methods you can use to predict positions of the minima:
(a) a graphic method, i.e. draw an interference pattern with proper scale for the
speakers’ separation and the wavelength.
(b) use the formula for angles θi at which minima should be observed:
sin (θi) = (i-½) λ / D, where i is an integer number.
Then, calculate dmin1, dmin2 from the formula: dmini = L tan ( θi )
.
Compare your predictions with the measured values. Do they agree?
(c) use the formula for angles θi at which maxima should be observed:
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sin (θi) = i λ / D, where i is an integer number.
Then, calculate dmax1 from the formula: dmax1 = L tan ( θi )
.
Compare your predictions with the measured values. Do they agree?
1.4
Observing Beats in Space (optional)
Beats in space are caused by a moving interference pattern. If the two speakers
are driven from two function generators, with slightly different frequencies, the
interference pattern no longer will be stable and the beats will be heard. However, if one
synchronizes his/her motion with that of the interference pattern, he/she may either not
hear beats or hear them with different frequency.
The students are encouraged to jog back and forth along the sidewalk, speeding
up or stopping the beats.
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