Vibrations and Waves s2

Chapter 19

Vibrations and Waves

There are two ways to transmit information/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

l is the length of the pendulum, g is the acceleration due to gravity (Galileo discovered this). Period (T) is independent of the bob mass.

Video - Three Bowling Balls

Video - Swinging Examples

Demo - Pendulum with extra mass

Pendulum Uses: Timing, Oil prospecting, Walking

When oscillations are small, the motion is called simple harmonic motion and can be described by a simple sine curve.

2. WAVE DESCRIPTION

Frequency (f) - the number of vibrations per unit of time made by the vibrating source.

Units - cycles per second, 1/s, Hertz (Hz)

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.

In symbolic form

T = 1/f or f = 1/T

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

URL - Transverse wave

A disturbance moves through the medium.

Elements of the medium vibrate.

Examples: ripples on water and wheat waves

4. WAVE SPEED

The average speed is defined as

For a wave, if the distance traveled is a wavelength (l), then the time to travel this distance is the period (T). Thus

is true for all waves.

Note: v is dictated by the medium.

f is dictated by the source.

Demo - Complete Bell Wave Machine

5. TRANSVERSE WAVES

Video - Slinky Transverse Waves

Examples: string musical instruments, ripples on water, electromagnetic waves

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

Example: sound in air

URL - Transverse & longitudinal waves

7. INTERFERENCE

Video - Superposition of Waves

Overhead - Interference

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.”

Demo - Rope and strobe

Demo - Mechanical overhead model

Video - Bell Wave Machine

Demo - Soda straw wave machine

Demo - Organ pipe and tuning fork

Another example: musical instruments

Video - Drumhead Vibrations

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 with Sound

Video - Doppler with Water

URL - Doppler Movie

When a source of waves and an observer of waves are getting closer together, the observer of the waves “sees” 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 “sees” 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.”

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.

Of course police use the Doppler effect to catch speeding motorists.

9. BOW WAVES

Waves in front of moving object pile up.

Overhead - Barrier slide

Overhead - “Bow” wave slide

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 - FB-111 Sonic Boom

Wav File - Sonic Boom

The boom is not produced just when the flying object “breaks” through the sound barrier.

Subsonic - slower than the speed of sound

Supersonic - faster than the speed of sound

Mach number = (speed of object)/(speed of sound)

Chapter 19

Demonstrations, Videos, and Slides

Demo - Metronome

Demo - Bowling ball pendulum

Video - Three Bowling Balls

Video - Swinging Examples

Demo - Pendulum with extra mass

Demo - Waves on a rope

URL - Transverse wave

Demo - Complete Bell Wave Machine

Video - Slinky Transverse Waves

Video - Slinky Longitudinal Waves