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 .