Introduction to Vibrations and Waves

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Vibrations and Waves

• Oar in Water
• Wings of a Bee
• Electrons in an Light Bulb

• Water Waves
• Sound Waves
• Light Waves

“Wiggles in Time”

“Wiggles in Space”

Vibrations and Waves

• Waves transmit energy and information.

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• Sound and Light are both waves.

Simple Harmonic Motion...

• …is to-and-fro vibratory motion.

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• ...results in sine curves.

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• 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

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• measured in seconds

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• Frequency - number of vibrations per unit time

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• measured in Hertz

Pendulums & Galileo

• The period does not depend on the amount of mass.

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• 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.

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Example Question

Changing which of the following affects the period of a pendulum?

• a) mass
• b) amplitude
• c) length
• d) angle

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What is the frequency in vibrations per second of a 60-Hz wave?

Answer: 60 cycles per second

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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

• medium - the stuff that carries the wave

Waves

Medium

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

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• It depends only on the type of medium.

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• Wave Speed = Frequency × Wavelength

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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.

1. What is the amplitude of the wave?

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• What is its wavelength?

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• How many nodes are there?

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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)

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INTERFERENCE

• Constructive or destructive interference results when waves add.

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• Standing Waves - wave pattern produced from interfering waves
• Examples
• Vibrating Strings in Lab
• Organ Pipe in Lab
• Bell Wave Machine in Class

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DOPPLER EFFECT

• the change in wavelength due to motion of the source

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• "Wheeeeeeeeeeee…….Oooooooooooooo”

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• Examples:
• moving cars and trains
• moving buzzer in a nerf ball (in class)
• rotating whistle

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

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

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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

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Question 3

The distance from trough to trough on a periodic wave is called its...

• a) frequency.
• b) period.
• c) wavelength.
• d) amplitude.

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Sound...

• ...a longitudinal wave in air caused by a vibrating object.

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• Sound requires a medium.
• solid, liquid or gas
• Sound waves have compression and rarefaction regions.

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Nature of Sound in Air

• Sound requires a medium.
• solid, liquid or gas
• Demo: Bell in a evacuated Bell Jar

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• Sound waves have compression and rarefaction regions.

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

Thanks