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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
Objects undergoing SHM trace out sine waves where the d is pos and neg with time.
Simple Pendulum
displacement– time graph w worksheet
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:
Vibrations & Waves
Waves are an energy disturbancepropagates through material or empty space.
Energy Transfer by Waves
Waves Transfer Energy
Matter is not transferredEx: Cork on water or buoy
Waves start with vibration
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?
-Can waves do work?
-Give examples.
Mechanical waves need medium through which to travel. Mediums include:
Gasses - air
liquids/water
Solids - wood
Ex: Sound/Earthquake waves
Non mechanical – no medium required!
Electromagnetic Waves (EM) need no medium
*EM waves can also propagate through a medium
Two Main Types of Waves
Transverse (all EM waves), seismic S waves
Longitudinal (Compressional)Sound, seismic P waves
Transverse Wave Pulse
One disturbance
Transverse Periodic WavePulses Pass at
Regular Intervals
Particles vibrate perpendicular to energy transport. Trace out sine wave.
Particle motion transverse wave.
Longitudinal/Compressional WaveParticles compressed and expanded parallel to energy propagation.
Another View
Sound Waves ex of mechanical wave. Need medium to propagate.
Vibrationsin air molecules from vibrating tuning fork or vibrating string.
Eardrumsound waves do work on eardrum
Water WavesCombination of 2 Types
Parts of a WaveWavelength distance btw Crests or TroughsMidpoint = Equilibrium Position
Crests
d
d
Wave Pulse• Single disturbance
Periodic Wave• Many pulses with regular
and period
1. State the difference between a mechanical and non-mechanical wave.
Longitudinal Wave Parts
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 = time to complete one cycle of wave crests or troughs. Time for disturbance to travel 1.
Usually measured in seconds.
T = 0.5 s/cycle.
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
f = how often T = how long f = a rate T = a time
T & f are inverse
f = 1/T or T = 1/f.
2. A wave has a period T of 5.0 seconds. What is its frequency?
0.2 hz
3. A wave has a frequency of 100 Hz. What is its period?
0.01 s.
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
Speed/Velocity = d/t
If a crest (or any point on a wave) moves 20m in 5 sec, v = 20m/5s = 4 m/s.
Relationship of wave speed to wavelength() and frequency(f).
v = d/t but for waves d = 1 occurs in time T (1period)
so v = /Tsince freq f =1/T
v =f
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.
= 0.081 m to 12 m
• Wave speed is constant if medium is uniform.
• Air at constant T and P.
• Homogenous solids.
• Water with constant T.
Only the medium through which it travels!
What determines wave speed?
7. A tuning fork produces a sound with f = 256 Hz and in air of 1.35 m.
• What is the speed of sound in air?
• What would be the wavelength of this tuning fork is sound travels through water at 1500 m/s?
• 346 m/s• 5.86 m
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.
8. What determines the wave’s frequency?
• Vibrational Rate
Example Problems & Hwk.Read Text 12 - 3
• Read Text Chap 12-3
• Do pg 470 #23- 32, 35, 36.
• Write all out will collect.
Do Now Text Pg 457 #2
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 position
What is the motion of points on a wave?
Up & down motion of particle on wave.
Another View
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
Wave Behaviors & Interactions Boundary Behavior & Wave
Superposition
When a wave enters a material with new properties it:
• Goes through it without noticing
• Slows down
• Speeds up
• Accelerates
Wave Behaviors and Interactions
Reflection- a wave incident on a boundary (new material), part bounces off, part transmitted.
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
Reflection off Fixed Boundary – pulse inverts
Reflection off Fixed Boundary – pulse inverts
Pulse Passing into new medium from less dense material. What happens to pulse?
Changes in:Velocity and Amplitude change with medium.
No Change - frequency.
More dense into less dense
How do multiple waves combine?
• Waves can overlap and occupy the same space at the same time.
• How they do it depends on the position or phase of the crests and troughs.
• Superposition – constructive destructive interference.
Phase of Particles in Wave
• “in phase” = points in identical position. Whole number of 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 apart. (A,D)
Superposition /Interference– 2 or more waves or pulses interact/superimpose & combine. Their amplitudes add or subtract.
The resultant wave is the sum of the two.
Constructive Interference
– waves superimpose with displacement in same direction + or -, amplitude increases.
Constructive Interference.
Destructive Interference- waves or pulses meet with opposite displacement. Waves partially or totally cancel.
Points on waves that meet “in phase” interfere constructively.
Points that meet “out of phase” interfere destructively. Below is total destructive interference.
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.
Standing Wave – wave appears to be standing still. No net transfer of energy.
Standing wave formed from wave pulses in same medium.
Nodes are points of max. destructive interference.
Antinodes = points of max. constructive interference.
Standing Wave Formation from 2 waves.
Standing waves have no net transfer of energy – no propagation of energy.
Sketch Resultant on wksht from RB pg 271.
Hwk Text pg 471 #33 - 44, 48-49
Hwk Text pg 471 #36 - 44, 48-50
Relation of Wavelength to String Length for Standing Waves
Standing waves form only when the string length allows a whole number of half wavelengths to fit.
½ = L or 2L = .
= L.
= L
General expression relating wavelength to string length for standing waves:
n ( ½ ) = L
n is a whole number
Mechanical Universe “Waves”