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PHY138 – Waves Lecture 9Quarter Review, including:
• Error Propagation• Simple Harmonic Motion: Force, Energy• Mass on spring / Pendulum• Damped Oscillations, Resonance• Traveling Waves, Power and Intensity• Standing Waves, Interference, Beats• Ray Model of Light, Ray-Tracing• Reflection, Refraction of Light• Thin Lens equation; Combination of Lenses
Tomorrow evening, 6:00 PM It is mandatory that you go to the room
assigned to your tutorial group. You should have no communication device
(phone, pager, etc.) within your reach or field of vision during the test.
The test has nine equally weighted multiple-choice questions (7 marks each).
The test has one multi-part problem counting for 37 marks; you must show your work.
Don’t forget… Your student card. A non-programmable calculator without
text storage and communication capability. A single original, handwritten 22 × 28
cm sheet of paper on which you have written anything you wish. We will supply any numerical constants you might need.
A dark-black, soft-lead 2B or 2HB pencil with an eraser.
Some more words to the wise… A good aid-sheet is well organized, easy to
read, and contains all the major equations from the assigned sections from the reading.
Copies of detailed specific problem solutions are unlikely to help.
Be ready to think; get a good night’s sleep tonight.
Keep in mind: Your best 3 out of 4 tests will count for 30% of your mark in the course.
The Eye
Propagation of Errors: good to have on aid sheet!!
z = A x Δz = A Δx
Mass on Spring versus Pendulum Mass on a
SpringPendulum
Condition for S.H.M.
Small oscillations
(spring obeys Hooke’s Law)
Small angles
(sinθ ≈ θ)
Natural frequency [rad/s]
Period
L
g
m
k
k
mT 2
g
LT 2
14.7 Damped Oscillations
Snapshot Graph
History Graph
Sinusoidal Wave Snapshot Graph
k = 2π/λ is the wave number
Sinusoidal Wave History Graph
ω=2π/T is the angular frequency
Sound Waves can be described either by the longitudinal displacement of the individual particles, or by the air or fluid pressure.
)sin(),( 0 tkxAxxtxD eqeqeq
)cos(),( 0max tkxPPPtxD atm
Electric and Magnetic fields, when oscillated, can create waves which carry energy. At certain frequencies, we see electro-magnetic waves as Light.
)sin(),( 00 tkxEtxE
)sin(),( 00 tkxBtxB
Power and Intensity The Power, P, of any wave source is how
much energy per second is radiated as waves [units = Watts]
The Intensity, I, is the energy rate per area. This determines how loud (sound) or bright (light) the wave is.
I=P/a, where a is an area perpendicular to the wave direction.
At a distance r from a small source, the intensity is I=P/(4πr2)
Doppler Effect
Principle of Superposition
If two or more waves combine at a given point, the resulting disturbance is the sum of the disturbances of the individual waves.
Two traveling waves can pass through each other without being destroyed or even altered!
Standing Wave:
The superposition of two 1-D sinusoidal waves traveling in opposite directions.
Harmonic frequencies of Standing WavesTransverse standing wave on a string
clamped at both ends: there are nodes in displacement at both ends.
,...)3,2,1(2
mL
vmfm
Standing sound wave in a tube open at both ends: there are nodes in pressure both ends.
,...)3,2,1(2
mL
vmfm
Wave Interference Two waves moving in the same direction
with the same amplitude and same frequency form a new wave with amplitude:
2
cos2
aA
where a is the amplitude of either of the individual waves, and is their phase difference.
Beat frequency Beats are loud sounds separated by soft sounds The beat frequency is the difference of the
frequencies of the two waves that are being added:
21mod2 ffffbeat The frequency of the actual sound is the
average of the frequencies of the two waves that are being added:
221 ff
favg
The Law of Reflection
11
Snell’s Law of Refraction
2211 sinsin nn
Total Internal Reflection
Can only occur when n2<n1
θc = critical angle.
When θ1 ≥ θc, no light is transmitted through the boundary; 100% reflection
1
2sinn
nc
Virtual Image Formation by Reflection
ss '
Virtual Image Formation by Refraction
sn
ns
1
2'
Real Image Formation with a Converging Lens
Focal length, f
Object
Real Image (inverted)