59. (a) To get to the detector, the wave from
S
1
travels a distance
x
and the wave from
S
2
travels a distance
√
d
2
+
x
2
. The phase diFerence (in terms of wavelengths) between the two waves is
p
d
2
+
x
2
−
x
=
mλ
m
=0
,
1
,
2
,...
where we are requiring constructive interference. The solution is
x
=
d
2
−
m
2
λ
2
2
mλ
.
We see that setting
m
= 0 in this expression produces
x
=
∞
; hence, the phase diFerence between
the waves when
P
is very far away is 0.
(b) The result of part (a) implies that the waves constructively interfere at
P
.
(c) As is particularly evident from our results in part (d), the phase diFerence increases as
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics

Click to edit the document details