Chapter 19 Vibrations and Waves

There are two ways to transmit information and energy in our universe: Particle Motion and Wave Motion

Light and Sound Both are vibrations of different kinds. Vibration - Wiggle in time Wave - Wiggle in space

1. VIBRATION OF A PENDULUM Demo - Metronome Demo - Bowling ball pendulum Video – Three Bowling Balls Video – Swinging Examples Demo - Pendulum with extra mass Time to swing depends on the length but not the mass of the pendulum.

Period of a Pendulum T is the period, the time for one vibration. l is the length of the pendulum. g is the acceleration due to gravity. Galileo discovered this. Period (T ) is independent of the mass of the bob.

Pendulum Uses: Timing Oil prospecting Walking When the oscillation is small, the motion is called simple harmonic motion and can be described by a simple sine curve.

2. WAVE DESCRIPTION Frequency ( f ) is the number of vibrations per unit of time made by the vibrating source. Units - cycles per second 1/s Hertz (Hz)

Picture of a Transverse Wave Crest l Wavelength A A - Amplitude Trough Baseline

Wavelength (l) Distance between adjacent crests in a transverse wave Distance a wave travels during one vibration Units - meters or feet

The period (T ) of a vibration is the time required to make one vibration. The period (T ) of a wave is the time required to generate one wave. It is also the time required for the wave to travel one wavelength.

Frequency Period

In symbolic form or

3. WAVE MOTION Energy is transported by particles or waves. A wave is a disturbance transmitted through a medium. Exception: light does not require a medium.

Demo – Waves on a rope A disturbance moves through the medium. Elements of the medium vibrate. Examples: ripples on water wheat waves

4. WAVE SPEED The average speed of anything is defined as

or Remember that Therefore For a wave, if the distance traveled is a wavelength (l), then the time to travel this distance is the period (T ). Then or Remember that Therefore

is true for all waves. Demo - Complete Bell Wave Machine Note: v is dictated by the medium. (must change medium to change v) f is dictated by the source. (must change the source to change f )

5. TRANSVERSE WAVES Video - Slinky Transverse Waves Examples: string musical instruments ripples on water electromagnetic waves Demo – Human Waves (Include Standing)

6. LONGITUDINAL WAVES Video - Slinky Longitudinal Waves Parameters Rarefactions are regions of low density. Compressions (condensations) are regions of high density. l is the distance between successive rarefactions or successive compressions.

Demo - Slinky Compressions Rarefactions Example: sound in air

7. INTERFERENCE Video - Superposition of Waves Slide - Interference

Interference

Constructive interference occurs when waves are in phase, that is when crests are superimposed and troughs are superimposed.

Destructive interference occurs when waves are out of phase, that is when crests are superimposed with troughs.

Interference is a characteristic of all waves.

Standing Waves When two sets of waves of equal amplitude and wavelength pass through each other in opposite directions, it is possible to create an interference pattern that looks like a wave that is “standing still.” It is a changing interference pattern. Demo - Rope and strobe

There is no vibration at a node. l There is no vibration at a node. There is maximum vibration at an antinode. l is twice the distance between successive nodes or successive antinotes.

Video - Drumhead Vibrations Demo - Organ pipe and tuning fork Demo – Standing waves in sheet metal Another example: musical instruments

8. DOPPLER EFFECT Refers to the change in frequency when there is relative motion between an observer of waves and the source of the waves

Video - Doppler Effect in Air Video - Doppler Effect in a Ripple Tank URL– Doppler Movie (htm) Demo – Doppler Rocket

When a source of waves and an observer of waves are getting closer together, the observer of the waves observes a frequency for the waves that is higher than the emitted frequency. When a source of waves and an observer of waves are getting farther apart, the observer of the waves observe a frequency for the waves that is lower than the emitted frequency.

All waves exhibit the Doppler effect. A particularly interesting example is used by astronomers to determine if light emitting objects (such as stars) are getting closer to us or farther away. On average most stars are moving farther away, and their light spectra are “red shifted.”

Red Shift Lab Absorption Spectrum of Element X Red Shifted Star Absorption Spectrum of Element X Star is moving away from us.

Police use the Doppler effect to catch speeding motorists. Radar bounced off a spinning planet can exhibit a Doppler effect and lead to a determination of the spin rate of the planet. This was used to discover that Venus has a retrograde spin.

Planet Spinning Under Cloud Cover

9. BOW WAVES Waves in front of moving object pile up. Wave Barrier

x x x x x x x

“Bow” Wave

x x x x x x x

The familiar bow wave generated by a speedboat knifing through the water is a non-periodic wave produced by the overlapping of many periodic circular waves. It has a constant shape.

10. SHOCK WAVES Just as circular waves move out from a swimming bug, spherical waves move out from a flying object. If the object flies faster than the waves, the result is a cone-shaped shock wave. Demo - Cone of Waves There are two booms, one from the front of the flying object and one from the back.

Demo – Crack whip Video – Sonic Booms Online Video - FB-111 Sonic Boom Video – F-14 Sonic Boom URL – More Boom Word Doc - Sonic Boom The boom is not produced just when the flying object “breaks” through the sound barrier.

Subsonic - slower than the speed of sound - faster than the speed of sound Supersonic speed of object Mach Number = speed of sound