Beats (lecture 10)
• Occur when two waves with equal amplitude and slightly different
frequencies interfere
• Periodic constructive and destructive interference causes
variations in loudness called beats
• The frequency of loudness variation or beat frequency is given by
f beat = f1 − f 2
PHYS 1901: Waves (Y&F Ch 13)
1
The Doppler Effect – Moving Listener
E.g., Parked car sounding the horn;
v + vo
v 

fo =
= 1 + o  f s
PHYS 1901:λWaves (Y&F
 Ch 13)v 
The cyclist hears frequency fo as he
approaches with speed vo
2
1
Moving Source and Moving Listener
fL =
v + vL
fS
v + vS
This expresses the
frequency heard by
the listener in terms
of the frequency of
the source
It includes all possibilities for motion of source and listener (relative to
the medium)
along
line joining them
PHYS 1901: Waves
(Y&Fthe
Ch 13)
3
Shock Waves
PHYS 1901: Waves (Y&F Ch 13)
4
2