Vibrations and Waves

Vibrations and Waves “Wiggles in Time” “Wiggles in Space” Water Waves Sound Waves Light Waves Oar in Water Wings of a Bee Electrons in an Light Bulb

Vibrations and Waves Waves transmit energy and information. Sound and Light are both waves.

Simple Harmonic Motion... …is to-and-fro vibratory motion. ...results in sine curves. Examples: metronome mass on a spring pendulum

Forces and vibrations Vibration - repetitive back and forth motion At the equilibrium position, spring is not compressed When disturbed from equilibrium position, restoring force acts toward equilibrium Carried by inertia past equilibrium to other extreme Example of “simple harmonic motion”

Describing vibrations Amplitude - maximum extent of displacement from equilibrium Cycle - one complete vibration Period - time for one cycle Frequency - number of cycles per second (units = hertz, Hz) Period and frequency inversely related

Description Period - the time required for one vibration measured in seconds Frequency - number of vibrations per unit time measured in Hertz Bowling Ball Example

Bowling Ball Example

Pendulums & Galileo The period does not depend on the amount of mass. The period does depend on the length of the pendulum.

* Example Test Question: If you double the frequency of a vibrating object, what happens to the period? a) the period doubles b) the period stays the same c) the period is cut in half d) not enough information is given to answer this question.

Example Question * Changing which of the following affects the period of a pendulum? a) mass b) amplitude c) length d) angle

What is the frequency in vibrations per second of a 60-Hz wave? Answer: 60 cycles per second What is its period? Answer: 1/60 second

Waves Periodic (traveling) disturbances transporting energy Causes Periodic motion disturbing surroundings Pulse disturbance of short duration Mechanical waves Require medium for propagation Waves move through medium Medium remains in place

Wave Motion Waves Medium medium - the stuff that carries the wave water waves water waves on a rope rope stadium waves people sound air light space (vacuum)

Wave Speed... the speed with which waves pass by a particular point e.g. the speed of a surfer It depends only on the type of medium. Wave Speed = Frequency  Wavelength Waves on a Rope Table in Notes – Appearance, Node, Antinodes, Wavelength, Frequency

Describing waves Graphical representation Pure harmonic waves = sines or cosines Wave terminology Wavelength Amplitude Frequency Period Wave propagation speed

Example Test Questions Answer these questions using the sine wave provided. What is the amplitude of the wave? What is its wavelength? How many nodes are there?

Example Wave 2 ½ meters 20 cm Amplitude = 10 cm Wavelength = 1 m Number of Nodes = 6

If a water wave oscillated up and down three times each second and the distance between wave crest is 2 m, what is its frequency? Answer: 3 Hz What is its period? Answer: 1/3 second What is its wavelength? Answer: 2 m What is its wave speed? Answer: 6 m/s

Kinds of waves, cont. Transverse waves Vibration direction perpendicular to wave propagation direction Example: plucked string Solids - support both longitudinal and transverse waves Surface water waves Combination of both Particle motion = circular

Kinds of waves Longitudinal waves Vibration direction parallel to wave propagation direction Particles in medium move closer together/farther apart Example: sound waves Gases and liquids - support only longitudinal waves

Waves in air Longitudinal waves only Large scale - swinging door creates macroscopic currents Small scale - tuning fork creates sound waves Series of condensations (overpressures) and rarefactions (underpressures)

INTERFERENCE Constructive or destructive interference results when waves add. Standing Waves - wave pattern produced from interfering waves Examples Vibrating Strings in Lab Organ Pipe in Lab Bell Wave Machine in Class http://www.kettering.edu/~drussell/Demos/superposition/superposition.html

http://www. kettering. edu/~drussell/Demos/superposition/superposition http://www.kettering.edu/~drussell/Demos/superposition/superposition.html

DOPPLER EFFECT the change in wavelength due to motion of the source "Wheeeeeeeeeeee…….Oooooooooooooo” Examples: moving cars and trains moving buzzer in a nerf ball (in class) rotating whistle Draw Doppler Picture

Sounds from moving sources Doppler effect Wave pattern changed by motion of source or observer Approaching - shifted to higher frequency Receding - shifted to lower frequency Supersonic speed - shock wave and sonic boom produced

http://www.kettering.edu/~drussell/Demos/doppler/doppler.html

Question 1 * A train whistle at rest has a frequency of 3000 Hertz. If you are standing still and observe the frequency to be 3010 Hertz, then you can conclude that... a) the train is moving away from you. b) the train is moving toward you c) the sound from the whistle has echoed d) not enough information is given

Question 2 * Dipping a finger in water faster and faster causes the wavelength of the spreading waves to a) increase b) decrease c) stay the same d) not enough information is given

Question 3 * The distance from trough to trough on a periodic wave is called its... a) frequency. b) period. c) wavelength. d) amplitude.

Sound... ...a longitudinal wave in air caused by a vibrating object. Sound requires a medium. solid, liquid or gas Sound waves have compression and rarefaction regions.

Nature of Sound in Air Sound requires a medium. solid, liquid or gas Demo: Bell in a evacuated Bell Jar Sound waves have compression and rarefaction regions.

Sound infrasonic ultrasonic human hearing range frequencies < 20 Hz frequencies between 20 Hz and 20,000 Hz

Sound waves Require medium for transmission Speed varies with Inertia of molecules Interaction strength Temperature Various speeds of sound

Velocity of sound in air Varies with temperature Warmer the air, greater the kinetic energy of the gas molecules Molecules of warmer air transmit sound impulses from molecule to molecule more rapidly Greater kinetic energy sound impulse transmitted faster Increase factor (units!): 0.6 m/s/°C; 2.0 ft/s/°C

SPEED OF SOUND How it varies: increases with humidity increases with temperature increases with density

Lightning and Thunder

What is the approximate distance of a thunderstorm when you note a 3 second delay between the flash of the lightning and the sound of the thunder? Answer: 3 seconds  340 meters/second = 1020 meters See blue questions on page 345. *

Sources of sound Vibrating objects Source of all sound Irregular, chaotic vibration produces noise Regular, controlled vibration can produce music All sound is a combination of pure frequencies

Vibrating strings Important concepts - strings with fixed ends More than one wave can be present at the same time Waves reflected and inverted at end points Interference occurs between incoming and reflected waves

Vibrating strings, cont. Standing waves Produced by interferences at resonant frequencies Nodes - destructive interference points Anti-nodes - points of constructive interference

Resonant frequencies of strings Fundamental - lowest frequency Higher modes - overtones (first, second, …) Mixture of fundamental and overtones produces “sound quality” of instrument Formula for resonant frequencies