Simple Harmonic and non harmonic Motion Amazing Pendulum Wave Effect Foucault's pendulum - Pantheon Paris

Chapter 12 Vibrations and Waves skipping 12.1 – Hooke’s law we already studied 12.2 Simple Harmonic Motion Any periodic, repetitive motion that involves a restoring force. Ex. A pendulum http://phet.colorado.edu/sims/pendulum-lab/pendulum-lab_en.html

T Amplitude – maximum displacement from equilibrium Or the height of a wave Period (T) - time per cycle – in seconds (s) Frequency (f) – number of cycles or vibrations per unit of time (inverse of Period) units – hertz (Hz) f= 1 T

The Period of a Pendulum depends on the pendulum length (L) and the free-fall acceleration (g) T = 2 π √L / g Period is independent of amplitude (for small amplitudes) Increase Length of a pendulum, increase the period. Decrease the length of the pendulum– decrease the period. Greater gravitational pull (Jupiter) – decrease the period (less time) Mass of the “bob” (weight) does not affect period.

12-3 Properties of Waves Waves carry energy from one place to another. Energy from a vibration travels through a ‘medium’. All phases of matter can act as a ‘medium’ (solid, liquid, and gas). Mechanical Waves - Waves that require a medium to travel. Most waves are mechanical waves.

Waves that do not require a medium to be transmitted are called electromagnetic waves (EM) (light, X-rays, ultraviolet light)

Sine wave – a wave whose source vibrates with simple harmonic motion described by a sine curve A Sine curve is pictorial representation of a periodic wave.

Waves are classified by the way they vibrate Transverse Waves particles in the wave move perpendicular to the direction the wave is traveling. Example: Wave on a rope, light and other electromagnetic waves, Also Earthquake waves – “S” waves – secondary waves http://www.youtube.com/watch?v=tWTVpeJ7krc Longitudinal Waves Motion of the medium is parallel to direction of wave. Example: sound waves, Also earthquakes waves – (compressional waves - “P” primary waves) Animation of S and P earthquake waves

P waves (compressional waves) also known as longitudinal waves – usual don’t cause as much damage as the S waves S waves (secondary wave) – shake the ground back and forth – perpendicular to the direction the wave is moving.

Surface waves – occur at the boundary between two different mediums – properties of both transverse and longitudinal waves – water waves are examples of surface waves Tsunami waves!

All waves share 3 basic characteristics: amplitude, wavelength, and frequency. Amplitude – maximum movement (distance) particles vibrate from rest. Wavelength – distance from one crest or trough to the next crest or trough. Measured in SI units of meters or centimeters. Symbol for wavelength = Greek letter lambda λ Frequency (f) number of waves per unit of time. (The number of vibrations per second) SI Unit = hertz (Hz). Larger the frequency smaller the wavelength.

Wave Speed Equation: (for all types of waves) Speed of Waves – dependent on type of ‘medium’ Denser the material, greater the velocity. Since Light travels 3.0 x 108 m/s, all electromagnetic waves (EM) travel at the same speed = speed of light. Sound waves travel slower than EM waves. Example: lighting and thunder. Wave speed is independent of amplitude and wavelength Wave Speed Equation: (for all types of waves) Speed = frequency x wavelength v = f x  Frequency is inversely proportional to wavelength

Quiz What is the time required for one wavelength to pass a given point? 2. What is the greatest distance particles are displaced from resting position? 3. What is the highest point of a transverse wave? 4. What is the distance from one crest to the next crest (or trough to trough) 5. What is the wave speed equation? 6. What is the relationship between period and frequency?

S = f x  speed (velocity) = frequency x wavelength Quiz What is the time required for one wavelength to pass a given point? period 2. What is the greatest distance particles are displaced from resting position? amplitude 3. What is the highest point of a transverse wave? crest 4. What is the distance from one crest to the next crest (or trough to trough) wavelength 5. What is the wave speed equation? S = f x  speed (velocity) = frequency x wavelength 6. What is the relationship between period and frequency? f = 1 / T

Wavelength, amplitude, period and frequency

Video: Transverse Waves

1994 Northridge Earthquake

Earthquake Magnitude Seismograms can be used to determine strength, or magnitude of an earthquake. Comparing the height of the wave (amplitude) to the time in sec The Richter Scale is used to measure the amount of energy released or (Magnitude of an Earthquake).

Seismograph seismogram

Each increase of one whole number of magnitude is equal to the release of 32 times more energy. Example: an earthquake of a magnitude 8.0 releases 32 x 32 (1024) times more energy than a magnitude 6.0

http://www.data.scec.org/significant/index.html http://earthquake.usgs.gov/earthquakes/map/

Liquefaction

What is your Seismic Risk? Mid West – Missouri – also can have strong earthquakes

12-4 Wave Interactions Mechanical Waves are displacement of matter Waves pass through each other - Form ‘interference patterns’ Wave Superposition - constructive interference and destructive interference

Constructive and Destructive interference

A Fixed boundary – waves are reflected and inverted

Standing wave pattern

Standing wave – a wave in constant position – two waves of the same frequency, wavelength, and amplitude travel in opposite directions and interfere. Harmonics in musical instruments are associated with a standing wave pattern http://www.youtube.com/watch?v=no7ZPPqtZEg Node - Point where 2 waves cancel – no motion Antinode – midway between two nodes, where the largest amplitude occurs. Standing Wave Example: Tacoma narrows Bridge in 1940 – standing waves caused by strong winds caused bridge to collapse

A teacher attaches a slinky to the wall and begins introducing pulses with different amplitudes. Which of the two pulses (A or B) below will travel from the hand to the wall in the least amount of time? They both travel at the same speed – the speed of the wave is only affected by the medium – not by the amplitude.

State Standards Addressed Waves: Waves have characteristic properties that do not depend on the type of wave. As a basis for understanding this concept: Students know waves carry energy from one place to another. Students know how to identify transverse and longitudinal waves in mechanical media, such as springs and ropes, and on the earth (seismic waves). Students know how to solve problems involving wavelength, frequency, and wave speed. Students know sound is a longitudinal wave whose speed depends on the properties of the medium in which it propagates. Students know radio waves, light, and X-rays are different wavelength bands in the spectrum of electromagnetic waves whose speed in a vacuum is approximately 3×108 m/s (186,000 miles/second). Students know how to identify the characteristic properties of waves: interference (beats), diffraction, refraction, Doppler effect, and polarization.