A little review

1
A little review

• Waves
• Two types, transverse and longitudinal
• Wave speed depends only on the medium
• Period, Frequency, Amplitude
• v ?f or v ? / T
• Interference
• Superposition-- adding waves
• Its all about Path Length Difference, ?, and..
• Sources in or out of Phase

2
Two Speakers or Two Slits
Wave troughs
Dark and bright fringes on a screen
Wave crests
Single frequency source
?
In phase at the slits
3
Two Speakers or Two Slits
Wave troughs
Does the pattern expand or contract when-the
slits move closer together?-the wavelength
increases?
Wave crests
Single frequency source
?
In phase at the slits
4
The ms (antinodes) ns(nodes)
0 zeroth order fringe
1 first order fringe
2 second order fringe
5
Always true for any interference problem
Sources In Phase
Constructive if PD m?
Destructive if PD (n ½ )?
PD path length difference n 1,2,3, n is
nodal line or dark line
m 0, 1, 2, 3,m is antinodal or bright line
6
Example Lets confirm PD
What is the PD for nodal and antinodal lines?
D1 ?
Two sources emit in phase ? ?
D2 ?
7
Two slit geometry (screen far away)
d
Screen
8
Two slit geometry
d
Screen
d sin?m m? constructive interference
d sin?n (n ½ )? destructive interference
When the sources (slits) are in phase
9
A simplified picture
Two slits very close together (d)
Screen very far away (L)
d sin?m m? constructive interference
d sin?n (n - 1/2)? destructive interference
When the sources (slits) and in phase
10
Distance between fringes, y
tan ? y/L Where y xm
m 2
n 2
m 1
n 1
L
?
m 0
n 1
m 1
d sin?m m? xm / L
n 2
d sin?n (n ½ ) ? xn / L
m 2
11
Example
m 2
n 2
m 1
n 1
5mm
?
m 0
2m
n 1
m 1
n 2
Light with a wavelength of 500 nm passes through
two closely spaced slits and forms an
interference pattern on a screen 2m away. The
distance between the central maximum and the
first order bright fringe is 5 mm. What is the
slit spacing? The light is in phase at the
slits.
m 2
d sin ? m? 1(500 nm)
tan ? 5mm / 2m
d 0.2 mm
? 0.14
12
Example
Twin radio antennas broadcast in phase at a
frequency of 93.7?MHz. Your antenna is located
150 m from one tower and 158 m from the other.
How is the reception, good or bad?
vwave??c??3?108 m/s
PD 8 m
Does this equal some m? or some (n - 1/2)? ?
v f ?
? 3.2m
Make two lists
0
1.6m n1
3.2m
4.8m n2
The condition is met for destructive
interference. Reception at that location is bad.
6.4m
8.0m n3
9.6m
11.2m n4
12.8m
14.4m n5