» 211 Syllabus

Unit 3 ; Topic Nine - Waves

-Topic 8:
      Oscillations : Ch.15 § 1,2,3
      . . . (HW due Tue.Nov.02)
      Pendulums & coupled Osc's : Ch.15 § 5 , 4
      . . . (HW due Fri.Nov.05)
    Quiz Mon.Nov.08

-Topic 9:
      Wave Propagation : Ch.16 § 1,2 ; Ch.17 § 1,2,3
      . . . (HW due Tue.Nov.09)
      Wave Interference : Ch.16 § 3,4 ; Ch.17 § 4,5
      . . . (HW due Thr.Nov.11)
  - plan for Exam 3 Mon.Nov.15 Fri.Nov.19 (or Thr.Nov.18)

propagation : ch.16 prob. 2,3,4,5,7,14(depth=?),21,23,27,32,24,36,37,51
length : ch.16 prob. 6,7,15,53,55,57,64,67,68,72,75
media motion : ch.16 prob. 9,10,11,42,43,47,49,76?
Doppler : ch.17 prob. 27,53,56,64
Intensity : ch.17 prob. 3,7,4,9,13,20,21,17,23 ; 47,48,50,52

Some Exam 3 Practice questions are available at mu-online (WebCT)

USE UNITS all thru your answer ... don't just append them onto the final number !
Put symbols on a sketch, as you read . . . use meaningful phrases : "v_match" , "catch" , "ground" "turn-around"
. . . show process spans as brackets or vector arrows , with words like   "average" , "losing" , "gaining" , "t=0→2" ...
Write statements as symbols first ... each statement has a SUBJECT ... manipulate symbols before plugging numbers.
. . . keep track of adjectives such as   "initial" , "average" , "final" , "stopped" . . . "change"

Topic 2 Reminders : (to topic 2 summary)

subscripts for "total" or "system" , "part A" ... keep track of the SOURCE for the external Forces applied to the (passive) object
Recognize whether you are predicting based on theory . . . reasoning from causes to their effects ... (what should it do?)
      or whether you are deducing from observation . . . (what does this imply about it?)
Get un-stuck (often) by wondering "why isn't it the same as it used to be?"

Topic 3 Reminders : (to topic 3 summary)
it's the Sum of external Forces that cause an object's mass to accelerate subscripts for "total" or "system" , "part A" ...
once you separate vectors into components, keep each component separate from the others!
ΣF = ma , for each component separately.

Topic 4 Reminders : (to topic 4 summary)
Name each Force by the source of that Force ... its cause ... a function of the environment.
spring Force : F_spring = − k s ... opposite the stretch vector .
Pressure Force : F_spring = P A   generally ... in a fluid , δP = ρ g δh .
Gravity : every mass in the universe contributes to the gravity field   g   at any place of interest.
... add "nearby" contributions as vectors ... g_{by M} = G M / r²_M-to-point (toward M) . . . then use   F_{gravity, on m} = mg ;       NOTICE : m ≠ M !

Topic 5 Reminders : (to topic 5 summary)

Energy is conserved quantity : Σ E_before   +   Σ W_{by F's not in PE list}   =   Σ E_after .
  KE = ½ m v² = ½ p·v = ½ p²/m   , in any of these equivalent forms .
Each Force either does Work during motion , or has an associated PE function ... not both .
=> W_{by F} = F·Δs .
=> − dU / dr = F_r , the component along that direction (r)
  PE_{gravity,local} = m g h , with h measured upward (z-direction) from a "zero-height reference" point
  PE_elastic = ½ k s²   . . . stretch s must be measured from its relaxed length
  PE_Pressure = P·V   ; it is okay to measure from a non-zero reference pressure , but be consistent !
  PE_Gravitation = − m GM / r .
  There IS NO PE for Friction Force ... must be explicitly included as a "Work by Forces not in the PE list"

Topic 6 Reminders : (to topic 6 summary)

Some Energy forms are somewhat complicated to calculate, at a fundamental level, such as Chemical PE or Nuclear PE.
. . . they can be treated as experimentally-measured quantities which are "released" (transformed) during some conversion process (i.e, burning).
      more material holds more Energy ; it is the PE density (PE/Volume) or the specific PE (PE/mass) that is measured.
efficiency is the fraction (or %) of the input Energy that is transformed into the "desired form".
. . . because total Energy is consserved, the sum of efficiencies in all output forms must be 100%.
Power is the rate that Energy is transformed (or transfered) into some other type (or to some other object)
=> P = ΔE / Δt , reported in [Watt] = [J/s] .
Because KE goes as v² = v_{x² + vy² + vz² , motion along each component adds in an independent manner .
. . . in particular, radial and angular motion components can be treated separately for objects in orbit
=> L = r × p is conserved then , so that   KEangular = L²/2mr²   is a useful formula .}

. . . r × F = Torque   τ . . . right-hand rist along r , fingers flip thru angle φ till point along F ; Thumb points ( | ) along Torque
. . . Torque is the angular analogy to (linear) Force => Σ τ = dL/dt . . . sometimes useful to write as   Σ τ = I α
Work (a scalar) is its own analogy ... W_rot = τ ·Δθ . . . Power   P = τ · ω
Kinetic Energy is its own analogy ... KE_rot = ½ I ω²   =   ½ L ω   =   L²/2I

Topic 8 Reminders : (to topic 8 summary)

massive objects often oscillate around their equilibrium location with natural frequency f = 1/T
... Energy will be (at least approximately) conserved , so KE will be maximum at the PE minimum , the equilibrium location.
... if PE = ½ k x² , the Time for the oscillation will be the same regardless of Amplitude
=> the oscillation angular frequency   ω_osc. [rad/sec] = √(k/m) .
      x(t) = A cos (ω t + φ) . . . <=> . . . x(t) = A cos (2 π t/T + φ) ;
      v(t) = − A ω sin (ω t + φ) . . . <=> . . . v(t) = − A (2 π/T) sin (2 π t/T + φ) ;
      a(t) = − A ω² cos (ω t + φ) . . . <=> . . . a(t) = − A (2 π/T)² cos (2 π t/T + φ) .
... Pendulums are gravity-driven oscillators, so the gravitational mass (in the PE) cancels the inertial mass (in ω's denominator)
      the PE's   "k" decreases as cos(θ) , so large angle amplitudes (>30°) take longer to oscillate.
=> small-angle pendulums oscillate with   ω_osc. ≈ √( (dτ/dθ) / I ) .
      . . . mass-on-string "simple" pendulum has   ω_osc. ≈ √(g/l) .