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Simple Harmonic Motion. Simple harmonic motion (SHM) refers an oscillatory, or wave-like motion that describes the behavior of many physical phenomena: a pendulum a bob attached to a spring low amp. waves in air, water, the ground vibration of a plucked guitar string.

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Presentation Transcript
slide2

Simple harmonic motion (SHM) refers an oscillatory, or wave-like motion that describes the behavior of many physical phenomena:

    • a pendulum
    • a bob attached to a spring
    • low amp. waves in air, water, the ground
    • vibration of a plucked guitar string
velocity and acceleration in shm
Velocity and acceleration in SHM
  • The position of an object undergoing SHM changes with time, thus it has a velocity
  • The velocity of an object is the slope of its graph of position vs. time. Thus, we can see that velocity in SHM also changes with time, and so object is accelerating:
some types of energy that travel as waves
Some Types of Energy that travel as Waves
  • Sound – vibrating tuning fork, string, wood etc.
  • Light (EM) – vibrating charges.
  • Earthquake – vibration of Earth’s crust
how can we prove that waves transfer energy

How can we prove that waves transfer energy?

Can waves do work?

Give examples.

slide14

Mechanicalwaves need medium through which to travel. Mediums include:

Gasses - air

liquids/water

Solids - wood

Ex: Sound/Earthquake waves

slide15
Non mechanical – no medium required!Electromagnetic Waves (EM) need no medium*EM waves can also propagate through a medium
slide17
Two Main Types of WavesTransverse (all EM waves), seismic S wavesLongitudinal (Compressional)Sound, seismic P waves
transverse wave pulse one disturbance
Transverse Wave Pulse

One disturbance

transverse periodic wave pulses pass at regular intervals

Transverse Periodic WavePulses Pass atRegular Intervals

Particles vibrate perpendicular to energy transport. Trace out sine wave.

longitudinal compressional wave particles compressed and expanded parallel to energy propagation
Longitudinal/Compressional WaveParticles compressed and expanded parallel to energy propagation.
sound waves ex of mechanical wave need medium to propagate
Sound Waves ex of mechanical wave. Need medium to propagate.

Vibrations

in air molecules from vibrating tuning fork or vibrating string.

parts of a wave wavelength l distance btw crests or troughs midpoint equilibrium position
Parts of a WaveWavelength (l) = distance btw Crests or TroughsMidpoint = Equilibrium Position
wave pulse
Wave Pulse
  • Single disturbance

Periodic Wave

  • Many pulses with regular l and period
transverse longitudinal waves can be represented by sine waves
Transverse & Longitudinal Waves can be represented by sine waves.

Longitudinal Waves can be graphed as density of particles vs time. Then will graph as sine wave.

period t frequency f

Period (T) & Frequency (f)

Period = time to complete one cycle of wave crests or troughs. Time for disturbance to travel 1l.

Usually measured in seconds.

T = 0.5 s/cycle.

slide33

Frequency = Number of cycles in unit time. Inverse of period.Usually number per second called Hertz (Hz)Ex: 3 crests or cycles per second = 3s-1 or 3 hz

4 the wave below shows a snapshot that lasted 4 0 seconds what is the frequency of the wave
4. The wave below shows a “snapshot” that lasted 4.0 seconds. What is the frequency of the wave?

4.0 seconds

2 cycles/4 s = 0.5 Hz

wave speed

Wave Speed

Speed/Velocity = d/t

If a crest (or any point on a wave) moves 20m in 5 sec, v = 20m/5s = 4 m/s.

slide39

Relationship of wave speed to wavelength(l) and frequency(f).v = d/t but for waves d = 1l occurs in time T (1period)so v = l/Tsince freq f =1/Tv =lf

slide40

5. A piano emits from 28 Hz to 4200 Hz. Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 m/s.

l = 0.081 m to 12 m

only the medium through which it travels

What determines wave speed?

Only the medium through which it travels!
  • Wave speed is constant if medium is uniform.
  • Air at constant T and P.
  • Homogenous solids.
  • Water with constant T.
slide43

Velocity depends on medium’s properties: -EM waves all travel at c in a vacuum.- EM waves slower through materials. -Vibrations travel faster on tighter strings - slower on loose strings.-v sound constant in air but depends on temp/density of air.

wave song
Wave song

http://www.youtube.com/watch?v=EzU79Egl3-c

example problems hwk read text 12 3
Example Problems & Hwk.Read Text 12 - 3
  • Read Text Chap 12-3
  • Do pg 470 #23- 32, 35.
  • Write all out will collect.
slide48
Quiz
  • 1. What is only factor that determines wave speed.
  • 2. Give a real life example of:
    • A longitudinal wave
    • A transverse wave.
  • Sketch a transverse wave. Label the
    • Wavelength
    • Amplitude
    • Equilibrium
when a wave enters a material with new properties it
When a wave enters a material with new properties it:
  • Goes through it without noticing
  • Slows down
  • Speeds up
  • Changes speed somehow.
slide53
Example Echo: A sound wave is traveling in air at STP. The echo is heard 2.6 second later. How far away is the reflecting object?
  • Time to object = 1.3 seconds.
  • Speed sound STP = 331 m/s
  • v = d/t
  • tv = d
  • (1.3s)(331 m/s)
  • 430.3 m
slide59

Superposition /Interference– 2 or more waves or pulses interact & combine. Their amplitudes add or subtract.

The resultant wave is the sum of the two.

constructive interference

Constructive Interference

– waves superimpose with displacement in same direction + or -, amplitude increases.

slide62
Destructive Interference- waves or pulses meet with opposite displacement. Waves partially or totally cancel.
slide63

Phase of Particles in Wave

  • “in phase” = points in identical position. Whole number of l apart.(A,F B,G E,J C,H)
  • 180o out of phase = equal displacement fr equilibrium but moving opposite directions.
  • Odd number of ½ l apart. (A,D)
points that meet out of phase interfere destructively below is total destructive interference
Points that meet “out of phase” interfere destructively. Below is total destructive interference.
sketch resultant on wksht from rb pg 271
Sketch Resultant on wksht from RB pg 271.

Hwk Text pg 471 #33 - 44, 48-49

slide69
Given a wave moving to the left as below, what will be the motion of the red beach ball just after the time shown?
  • Up
  • Down
  • Right
  • Left

Down

slide70

Standing WavesWave pattern that results when 2 waves, of same f, & v travel in opposite directions. Often formed from pulses reflected off a boundary. Waves interfere constructively & destructively at fixed points.

slide73

Nodes are points of max. destructive interference.Antinodes = points of max. constructive interference.

standing waves form only when the string length allows a whole number of half wavelengths to fit
Standing waves form only when the string length allows a whole number of half wavelengths to fit.
general expression relating wavelength to string length for standing waves

General expression relating wavelength to string length for standing waves:

n ( ½ l) = L

n is a whole number