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 –vibration of a plucked guitar string

Objects undergoing SHM trace out sine waves where the d is pos and neg with time.

Simple Pendulum

D – t graphe Velocity & acceleration SHM The position of an object undergoing SHM changes with time, thus it has a velocity. Mark d and t on axis. Where is the velocity on this graph? Where is the velocity approximately constant? Where is acceleration maximum?

Vibrations & Waves

Energy Transfer by Waves Waves are an energy disturbance propagates through material or empty space. Waves Transfer Energy. Matter is not transferred. How can we prove it?

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

Vocabulary: Mechanical waves - need medium through which to travel. Mediums include: Gasses - air liquids/water Solids – wood Examples: Sound/Earthquake waves

Non mechanical – no medium required! Electromagnetic Waves (EM) need no medium *EM waves can also propagate through a medium. See table!

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 Wave Pulses Pass at Regular Intervals Particles vibrate perpendicular to energy transport. Trace out sine wave.

Particle motion transverse wave.

Longitudinal/Compressional Wave Particles compressed and expanded parallel to energy propagation.

Another View

Sound Waves ex of mechanical wave. Need medium to propagate. Vibrations in air molecules from vibrating tuning fork or vibrating string.

Eardrum sound waves do work on eardrum

Parts of a Wave Wavelength  distance btw Crests or Troughs Midpoint = Equilibrium Position

Crests d d

Wave Pulse Single disturbance Periodic/traveling 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/Tor 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/tbut for waves d = 1 occurs in time T (1period) so v = /T since freqf =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. = 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?

6. All EM waves travel at 3 x 10 8 m/s in space. A particular EM wave has a wavelength, of 5.2 x m. a. Calculate its frequency. b. Calculate its period. c. Use your table to identify the specific type of wave it is x Hz x Hz.

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 only on medium’s properties: EM waves all travel at c in a vacuum EM waves are 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 Frequency is fixed by the source.

Wave song 3:30 Mechanical Universe Waves – 29 min

Example Problems & Hwk. Read Text Read Text Chap 12-3 Do pg 470 # skip 31 Write all out will collect.

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.

10. 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) m

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 pulses or 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 results in destructive interference.

Phase of Particles in Wave In phase = points in identical position different pulses. Whole number of apart.(A,F B,G E,J C,H). out of phase points are opposite = 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 – meet in phase.

Destructive Interference- waves or pulses meet with opposite displacement – out of phase. Waves partially or totally cancel.

Star review page 271 superposition sketch w ruler.

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

Standing Waves describe it Standing Wave – wave appears to be standing still. No net transfer of energy.

Standing wave formed from wave pulses in same medium.

Pattern resulting 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. Demo

Nodes are points of max. destructive interference. Antinodes = points of max. constructive interference. How many wavelengths ( ) ? Half wavelengths ( ), distance between nodes! Whole, 2 nodes!

Questions Name the points and label the standing wave pattern. How many wavelengths are there in the standing wave above? How many nodes above?

Standing waves have no net transfer of energy – no propagation of energy.

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

Mechanical Universe “Waves” Hwk Read 12-3, 12 – 4. Text Pg 457 #2, 3 And pg 471 #31,

Standing Wave Formation from 2 waves.

Hwk Read Text 12 – 3, 12 – 4. Do pg 471 # Full sentences, show work.