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### Chapter 19

Vibrations and Waves

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.

- 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.

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

Units -

cycles per second

1/s

Hertz (Hz)

2. WAVE DESCRIPTIONDistance between adjacent crests in a transverse wave

Distance a wave travels during one vibration

- meters or feet

Wavelength (l)Units

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

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.

wheat waves

Demo – Waves on a rope

A disturbance moves through the medium.

Elements of the medium vibrate.

Examples:

Doubling the mass of a simple pendulum undergoing small oscillations does what to the period of the pendulum?

(a) cuts it in half

(b) increases it by the square of 2

(c) nothing

(d) doubles it

4. WAVE SPEED

The average speed of anything is defined as

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

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 )

Video - Slinky Transverse Waves

Examples:

string musical instruments

ripples on water

electromagnetic waves

5. TRANSVERSE WAVES6. 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.

What dictates the frequency of a sound wave?

(a) wavelength

(b) medium

(c) source of the sound

(d) speed

(e) amplitude

What determines the speed of a wave?

(a) the frequency

(b) the wavelength

(c) the amplitude

(d) the period

(e) the medium of transmission

A skipper on a boat notices wave crests passing his anchor chain every 5 seconds. If the wave crests are 15 m apart, what is the speed of the water waves in m/s?

(a) 5

(b) 15

(c) 75

(d) 10

(e) 3

For a medium transmitting a longitudinal wave, the areas of the medium where the density of the medium is temporarily increased are called

(a) rarefactions

(b) compressions

(c) density holes

Interference

Applet

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.

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.

There is maximum vibration at an antinode.

l is twice the distance between successive nodes or successive antinotes.

l

- 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.”

Lab Absorption Spectrum of Element X

Star Absorption Spectrum of Element X

Red Shifted

Red ShiftStar 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.

When you move away from a fixed source of sound, the frequency of the sound you hear

(a) is greater than what the source emits

(b) is less than what the source emits

(c) is the same as what the source emits

9. BOW WAVES

- Waves in front of moving object pile up.
- Wave Barrier

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
- 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.

Sonic booms from a plane are produced

(a) because the plane breaks through the sound barrier

(b) when the plane reaches the speed of sound

(c) by the plane traveling faster than the speed of sound

(d) by the plane traveling slower than the speed of sound

- slower than the speed of sound

Supersonic

Subsonic- faster than the speed of sound

speed of object

Mach Number

=

speed of sound

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