Announcements
Announcements
1. HW11 due April 22
3. Final exam:
April 25, Saturday, 10 am to noon
2. Make-up exam:
April 22 Wednesday, 7:20 – 9:10 pm, meet at Prof. Reitze’s
office (NPB 2265)
Room assignments:
last name
room
covers all material in the course.
A-GAR
computer science engineering A101
To take the make-up exam, you must obtain permission
from Prof. Chan or Prof. Reitze.
GEE-J
Fine Arts B 105
K-MAZ
Florida Gym 230
MCC-O
Florida Gym 260
P-R
Florida Gym 280
S-Z
Williamson 100
roughly ½ of questions on topics covered in midterms,
the rest on Chapters 9, 13, 14
Simple pendulum from last lecture
13. Vibrations and Waves
Clarification between period and tension
Found everywhere in the universe and in daily life.
• hearing and vision.
• Ultrasound diagnostics.
L
g
T = 2π
Period, not tension
Image: Absorption, Transmission,
and Reflection of ultrasound
Waves: Chapter 13.4-13.7
Transverse wave
Wave velocity
Each part of spring moves
⊥ to wave velocity
λ
Simple harmonic motion
X direction (space/not time)
Longitudinal or compression wave
Wave velocity
y
λ
x
λ = wavelength
Waves
1
Chapter 14
Wave motion-Wave velocity c
c
ct
Tuning Forks produce single frequency sound
c = λ/T = λƒ
Always true:
Light-transverse
Sound-longitudinal
Any wave
λ
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
• 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
Wavefronts
Planar wave front
spherical wave front
Distance between wavefronts = λ
Speed of Sound
Liquid
v =
»B is the Bulk Modulus of the liquid
B
»ρ is the density of the liquid
ρ
Solid Rod
Y ¾Y is the Young’s Modulus of the
v=
ρ material
¾ρ is the density of the material
In General
v=
elastic property
inertial property
Doppler Effect-Source in Motion
• As the source moves
toward the observer (A),
the wavelength appears
shorter and the
frequency increases:
• 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 ⎠
2
Doppler Effect -Observer moving-Source stationary
• Goes toward source
• Encounters more wave
fronts per second-closer
together
• The frequency heard is
increased
• Goes away from source
• The observer detects
fewer wave fronts per
second-farther apart
• The frequency sounds
lower
Doppler Effect-General Case
⎛ v + vo ⎞
ƒo = ƒ s ⎜
⎟
⎝ v ⎠
⎛ v ⎞
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
⎛ v + vo ⎞
ƒo = ƒ s ⎜
⎟
⎝ v ⎠
• Both the source and the observer could be
moving
⎛ v + vo ⎞
ƒo = ƒ s ⎜
⎟
⎝ v − vs ⎠
Product of the two equations
Speed of Sound in Air
m⎞
T
⎛
v = ⎜ 331 ⎟
s
273
K
⎝
⎠
T is absolute
temperature in Kelvin
= °C + 273
3