Chapter 13.4-13.5; 13.7-13.8
Announcements
The whole universe is composed of SHOs
1. Make-up exam is Dec. 9 at 8 pm in NPB 1101.
Comprehensive-problems like homework from all chapter
sections studied.
2. HW 11 due Tuesday (Dec. 8) at 11:59 pm
3. Please pick up your exam forms, here and from file
cabinet in Tutorial Room.
4. Final Exam concentrates on material since Exam 2, but
has homework-like problems from all chapters as follows:
All in Ch. 1 to 5; 6.1 to 6.4; 7.1 to 7.5; 8; 9.1 to 9.7;
13.1 to 13.5; 13.7 to 13.8; 14.1 to 14.3; and 14.6
SHO is system with linear restoring force to original shape/position
Note: For a mass/spring a = - k x / m not constant
True for all oscillators
Mass/spring
1 ω
Frequency f = =
T 2π
Oscillators make Waves
ωms
k
=
m
ωp =
g
L
Wave motion-Wave velocity v
All waves carry energy and momentum
Types of Waves – Transverse
Pendulum
c
ct
Wave velocity
v = λƒ
Each part of spring moves
⊥To wave motion
Like AM radio
λ
X direction (space/not time)
Longitudinal or compression wave
Wave velocity
λ
Chapter 14.1-14.3; 14.6
Tuning Forks produce single frequency sound
• As the tuning fork vibrates, a succession of
compressions and rarefactions spread out from the
fork
• A sinusoidal curve can be used to represent the
longitudinal wave
– Crests correspond to compressions and troughs
to rarefactions
Always true:
Light-transverse
Sound-longitudinal
Any wave
λ
Most waves need a medium-Except light
Categories of Sound Waves
• Audible waves
– human hearing:
Normally between 20 Hz to 20,000 Hz
• Infrasonic waves
– Frequencies are below the audible rangeEarthquakes or car stereos
• Ultrasonic waves
– Frequencies are above the audible range
Dog whistles
1
Speed of Sound
Liquid
B » B is the Bulk Modulus of the liquid
v =
ρ » ρ is the density of the liquid
Solid Rod
Y Y is the Young’s Modulus of the material
v=
ρ ρ is the density of the material
In General
v=
elastic property
inertial property
Table 14.1, p. 462
Speed of Sound in Air
m
T

v =  331 
273
s
K


T is absolute temperature
in Kelvin
= °C + 273
Doppler Effect -Observer moving-Source stationary
• Observer goes toward source
• Encounters more wave fronts
per second-closer together
• The frequency heard is
 v + vo 
increased
ƒo = ƒs 


v

• Observer goes away from source
• The observer detects fewer wave
fronts per second-farther apart
• The frequency sounds lower
 v − vo 
ƒo = ƒ s 

 v 
Doppler Effect-Source in Motion
• As the source moves
toward the observer (A),
the wavelength appears
shorter and the frequency
increases: v
= λƒ
 v 
ƒo = ƒ s 

 v − vs 
•As the source moves away
from the observer (B), the
wavelength appears longer
and the frequency appears
to be lower
 v 
ƒo = ƒ s 

 v + vs 
Doppler Effect-General Case
• Both the source and the observer could be
moving
 v + vo 
ƒo = ƒ s 

 v − vs 
• Use positive values of vo and vs if the motion is
toward each other--Frequency appears higher
• Use negative values of vo and vs if the motion is
away from each other--Frequency appears lower
Above is product of the two previous equations:
 v + vo 
ƒS’o = ƒ s 

 v 
 v 
ƒo = ƒ s 

 v − vs 
2