12: PRELAB: INTERFERENCE
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, cancelling 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 _ 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 _ meters. Therefore, the
difference in the two path lengths is d = 0.5m. Constructive interference will occur when
d = _, 2_, 3_, 4_, … , where _ is the wavelength. Use the relation v = _ f, (v – speed of
sound, f – frequency) to complete calculations of 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 = _ _, (1+_) _, (2+_)_ , …) will occur.
Case
Constructive interference
Destructive interference
 f1 = v/_ = 688 Hz;
_ = 2d = 1 m
 f 1 = 344 Hz
1.
_ = d = 0.5 m
2.
_ = d/2 = 0.25 m  f2 =
Hz;
_ = 2d/3 = 0.33m  f 2 =
Hz
3.
_=
 f3 =
Hz;
_ =
 f3 =
Hz
4.
_=
 f4 =
Hz;
_ =
 f4 =
Hz
12: Interference Prelab - 1
Excerpts from an article on microphone placing:
Another example of the interference idea, and one of practical value, is the question of hte
microphone placement when using a public address system. Consider a group of people sitting around a
table with the microphone placed somewhere in the center. Should the mike be placed on a stand, or should
it be laid directly on the table top itself as shown in Fig. 1? Almost everyone, without even thinking, will
answer that the stand is the more favorable setup because that is the way it is usually done. However,
almost everyone is wrong! As we shall now show, the use of the table-plus-stand can lead to an undesirable
partial sound cancellation caused by destructive interference at certain frequencies. To understand this we
only need to remember that sound arrives at the mike via two paths: (a) directly from the speaker, and (b)
along a path that has been reflected from the table top as indicated in Fig. 2. The arrival of these two waves
should arouse your suspicions because the two will overlap at the mike and the conditions for either
constructive or destructive interference might be right. For example, if the path of the reflected wave is one
half of a wavelength longer than that of the direct wave, the two waves will arrive out of phase. A partial
cancellation results in this case because the two waves, in general, may not be equally loud, and hence,
their amplitudes would not be the same.
An example of Microphone Placement
Fig. 1: Should the microphone be placed
directly on the top of the table or should
a microphone stand be used?
Fig. 2: The direct and reflected sound
waves arrive at the mike by two
different paths. Interference between the
two waves will occur.
To illustrate this problem, suppose the direct sound travels 2 meters and the reflected sound covers
a greater distance of 2.5 meters. Now, as a person speaks, the voice emits different frequencies within the
audio range, and each of these frequencies will give rise to direct and reflected sounds. Fro the sound wave
whose frequency is 344 Hz, the conditions are perfect for destructive interference since, like the speaker
example, the reflected wave travels one-half a wavelength or 0.5 meters, further. The sound intensity
reaching the microphone might look something like Fig. 3.. The figure shows that the sound near 344 Hz is
substantially quieter than normal because of the destructive interference that has occurred between the
direct and reflected waves. Therefore the voices, as amplified by the public address system, will sound
unnatural due to the loudness "hole" near 344 Hz.
While the 344 Hz tone suffers a loss in intensity due to destructive interference, the 688 Hz tone
will exhibit constructive interference and, hence, produce a louder than normal sound at the mike. The
reason for the constructive interference is that the wavelength of the 688 Hz sound is 0.5 meters, which is
precisely the path difference between the direct and reflected sounds. A path difference of one whole
wavelength causes the waves to arrive in-phase at the mike. Figure 3 shows a "bump" in the frequency
response curve at 688 Hz that implies that the sound at this frequency will be louder than normal and will,
once again, appear unnatural.
What is the solution to the problem of destructive and constructive interference? Simple. Place the
microphone directly on the tabletop thereby forcing the direct and reflected waves to travel the same
distance. The two waves will always arrive at the microphone in-phase regardless of their frequency. There
will never be an out-of-phase condition eliminating part of the sound. By this manner the microphone is
12: Interference Prelab - 2
more efficient picking up the sound. Therefore, either place a microphone very close to, or very far away
from, a reflecting surface in order to avoid destructive interference problems.
Some of the sound
intensity here has been
lost due to destructive
interference between the
direct and reflected waves
50
344
Constructive
interference
688
Frequency [Hz]
Fig. 3: Interference can produce a partial cancellation of the sound
at certain frequencies or an enhancement at other frequencies, depending
on whether the waves are in-phase or out-of-phase when they reach the mike.
12: Interference Prelab - 3
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.
12: Interference Prelab - 4
Line through crossing points
mark points of maximum amplitude
Example Interference
Pattern
Source 1
Source 2
Circles of
high pressure
Scale
12: Interference Prelab - 5
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.
Source 1
Source 2
Scale
12: Interference Prelab - 6