Simple Harmonic Motion

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# Simple Harmonic Motion - PowerPoint PPT Presentation

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

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
• 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
• 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.

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 WavesTransverse (all EM waves), seismic S wavesLongitudinal (Compressional)Sound, seismic P waves
Transverse Wave Pulse

One disturbance

### Transverse Periodic WavePulses Pass atRegular Intervals

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

Longitudinal/Compressional WaveParticles compressed and expanded parallel to energy propagation.
Sound Waves ex of mechanical wave. Need medium to propagate.

Vibrations

in air molecules from vibrating tuning fork or vibrating string.

Parts of a WaveWavelength (l) = distance btw Crests or TroughsMidpoint = Equilibrium Position
Wave Pulse
• Single disturbance

Periodic Wave

• Many pulses with regular l and period

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 1l.

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

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(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

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

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.

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

Example Problems & Hwk.Read Text 12 - 3
• Do pg 470 #23- 32, 35.
• 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
When a wave enters a material with new properties it:
• Goes through it without noticing
• Slows down
• Speeds up
• Changes speed somehow.
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

### 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

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

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

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.
Sketch Resultant on wksht from RB pg 271.

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

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

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.

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.

### General expression relating wavelength to string length for standing waves:

n ( ½ l) = L

n is a whole number