76. Let the frequencies of sound heard by the person from the left and right forks be f
l
and f
r
, respectively.
(a) If the speeds of both forks are u, then f
l,r
= f v/(v
± u) and
f
beat
=
|f
r
− f
l
| = fv
1
v
− u
−
1
v + u
=
2f uv
v
2
− u
2
=
2(440 Hz)(30.0 m/s)(343 m/s)
(343 m/s)
2
− (30.0 m/s)
2
=
77.6 Hz .
(b) If the speed of the listener is u, then f
l,r
= f (v
± u)/v and
f
beat
=
|f
l
− f
r
| = 2f
u
v
= 2(440 Hz)
30.0 m/s
343 m/s
= 77.0 Hz .