26-1
I
NTERFERENCE AND
D
IFFRACTION
26
Answers to Multiple-Choice Problems
1.
C
2.
A, C, D
3.
B
4.
C
5.
A
6.
A
7.
B
8.
A
9.
C
10.
B
11.
A
12.
B
13.
D
14.
C
15.
C
Solutions to Problems
26.1.
Set Up:
Constructive interference occurs for
Destructive interference
occurs for
For this problem,
and
The path taken by
the person ensures that
x
is in the range
Solve: (a)
For
1, 2, 3, 4 the values of
x
are 150 cm,
116 cm, 82 cm, 48 cm, 14 cm.
(b)
For
1, 2, 3 the values of
x
are 133 cm,
99 cm, 65 cm, 31 cm.
Reflect:
When
the path difference is
which is one wavelength. When
the path difference is 17 cm, which is one-half wavelength.
26.2.
Set Up:
For radio waves,
Constructive interference occurs for
Destructive interference occurs for
For this problem,
and
The path taken by the person
ensures that
x
is greater than 50.0 m.
Solve: (a)
For
1, 2, 3, 4,
53.3 m, 56.5 m,
59.8 m, 63.0 cm.
(b)
For
1, 2, 3, 4,
54.9 m,
58.2 m, 61.4 m, 64.7 m.
26.3.
Set Up:
The nature of the interference depends on the path difference.
Solve: (a)
The person is a distance
from
A
and a distance
from
B
. The path difference is
The interference is determined by
D
and is independent of
d
.
(b)
No, the loudness won’t change. As he walks, the path difference remains constant.
26.4.
Set Up:
When she is at the midpoint between the two speakers the path difference
is zero. When she
walks a distance
d
toward one speaker,
increases by
d
and
decreases by
d
, so the path difference changes by 2
d
.
gives constructive interference and
gives destructive interference.
6
2,
c
.
6
1,
m
5
0,
path difference
5
A
m
1
1
2
B
l
,
6
2,
c
.
6
1,
m
5
0,
path difference
5
m
l
,
r
1
r
2
r
2
2
r
1
r
A
2
r
B
5
D
1
d
2
d
5
D
.
r
B
5
d
r
A
5
D
1
d
x
5
51.6 m,
m
5
0,
x
5
50.0 m
1
A
m
1
1
2
B
1
3.26 m
2
.
x
2
50.0 m
5
A
m
1
1
2
B
1
3.26 m
2
.
x
5
50.0 m,
m
5
0,
x
5
50.0 m
1
m
1
3.26 m
2
.
x
2
50.0 m
5
m
1
3.26 m
2
.
r
1
5
50.0 m.
r
2
5
x
6
2,
c
.
6
1,
m
5
0,
r
2
2
r
1
5
A
m
1
1
2
B
l
,
6
2,
c
.
6
1,
m
5
0,
r
2
2
r
1
5
m
l
,
l 5
v
f
5
3.00
3
10
8
m
/
s
92.0
3
10
6
Hz
5
3.26 m.
v
5
3.00
3
10
8
m
/
s.
x
5
133 cm
150 cm
2
116 cm
5
34 cm,
x
5
116 cm
m
5
0,
x
5
150 cm
2
A
m
1
1
2
B
1
34 cm
2
.
150 cm
2
x
5
A
m
1
1
2
B
1
34 cm
2
.
m
5
0,
x
5
150 cm
2
m
1
34 cm
2
.
150 cm
2
x
5
m
1
34 cm
2
.
0
#
x
#
150 cm.
r
1
5
x
.
r
2
5
150 cm
6
2,
c
.
6
1,
m
5
0,
r
2
2
r
1
5
A
m
1
1
2
B
l
,
6
2,
c
.
6
1,
m
5
0,
r
2
2
r
1
5
m
l
,