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Waves and Vibrations

Adapted from

Physics: Mr. Maloneyhttp://web.mit.edu/nelsongroup/outreach/docs/waves.ppt

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Waves are everywhere in nature

Sound waves, visible light

waves, radio waves, microwaves, water waves, sine waves,

telephone cord waves,

stadium waves,

earthquake waves,

waves on a string,

slinky waves

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What is a mechanical wave?

a mechanical wave is a disturbance that travels through a medium from one location to another

a mechanical wave is the motion of a disturbance

mechanical waves differ from electromagnetic (EM) waves, because EM waves do not require a medium to travel

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How can we model mechanical waves?

Follow the path around the room to investigate the cause, types, and properties of mechanical waves

Record notes, observations, and data on the front of your “journal”

Answer the checkpoint questions on the back of your “journal”

Stop what you are doing and answer the quick checks using your Plickers card

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Slinky Wave

Let’s use a slinky wave as an exampleWhen the slinky is stretched from end to

end and is held at rest, it assumes a natural position known as the equilibrium or rest position

To introduce a wave here we must first create a disturbance

We must move a particle away from its rest position

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Slinky Wave

One way to do this is to jerk the slinky forwardthe beginning of the slinky moves away from its

equilibrium position and then backthe disturbance continues down the slinkythis disturbance that moves down the slinky is

called a pulseif we keep “pulsing” the slinky back and forth,

we could get a repeating disturbance

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Slinky WaveThis disturbance would look something like this

This type of wave is called a LONGITUDINAL wave

The pulse is transferred through the medium of the slinky, but the slinky itself does not actually move

It is just disturbed from its rest position and then returns to it

So what really is being transferred?

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Slinky WaveEnergy is being transferredThe metal of the slinky is the MEDIUM that

transfers the energy pulse of the waveThe medium ends up in the same place as it

started … it just gets disturbed and then returns to its rest position

You used energy to create a disturbance on the end of the slinky. This energy was transferred the length of the slinky in the form of a wave. The particles of the medium were disturbed, but were not displaced (start and end point are the same)

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Longitudinal Wave

Let’s take a look at this longitudinal wave.The medium particles vibrate parallel to the

motion of the pulseAreas of the medium with high density

(PRESSED together) are called compressionsAreas of the medium with low density (RARE to

see FACTIONS of particles together) are called rarefactions

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Longitudinal WaveSound waves are longitudinal wavesThe membrane of a speaker moves to create the

disturbance of air particles (the medium), and this disturbance continues to travel through the medium (air particles compress and then return to rest position)

Draw It! Use dots to represent air particles and make a drawing of repeating compressions (high density) and rarefactions (low density) created by a vibrating speaker

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Longitudinal WaveStill have questions? Watch the video to learn

more about longitudinal waves

Checkpoint QuestionsExplain how waves transfer energy without

transferring matter.Explain the relationship between the direction of

the disturbance, medium movement, wave movement, and energy transfer in a longitudinal wave.

Compare and contrast compressions and rarefactions.

Why can’t sound waves travel in outer space?

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Transverse waves

A second type of wave is a transverse wave

We said in a longitudinal wave the pulse travels in a direction parallel to the disturbance

In a transverse wave the pulse travels perpendicular to the disturbance

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Transverse WavesThe direction of the disturbance determines

the motion of the medium, but the direction of the wave (and energy) remains the same

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Transverse WavesYou can produce transverse waves with

the slinky (try it!)To break the disturbance down into parts,

we are going to use the bead stringWe will be drawing the locations of the

beads on your paper with different color highlights representing different phases of the disturbance

Be sure to try the movements a few times to observe position and direction of each bead before drawing it

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Transverse WavesEquilibrium or Rest Position – lay the

bead string out along the “x-axis” of your paper and mark the position of the beads by placing a dash under each bead

Crest – move the end of your string up the “y-axis” and stop at the “top”

Mark the locations of your beads with a different color highlighter

Trough – move the end of your string down the “y-axis” and stop at the “bottom” (go as far below the equilibrium as you went above)

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Transverse WavesMark the locations of your beads with a

different color highlighterAdd arrows to show if the beads moved up

or down (use the previous position marks as a reference)

Return to Rest Positon (EquilibriumMark the locations of your beads with a

different color highlighterAdd arrows to show if the beads moved up

or down (use the previous position marks as a reference)

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Transverse WavesThe motion of the disturbance was

perpendicular (transverse) One wave was created from the cycle of up

to crest, down to trough, back to equilibriumOne cycle produces one pulseIf you keep doing it periodically over and

over again, the motion creates periodic waves

Periodic motion creates waves (pulses) that repeat at regular time intervals (periods)

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Transverse WavesCheckpoint Questions

Explain how waves transfer energy without transferring matter.

Explain the relationship between the direction of the disturbance, medium movement, wave movement, and energy transfer in a transverse wave.

How can the different types of waves be described in terms of movement and energy?

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Anatomy of a Wave

Now we can begin to describe the anatomy of our waves

We will use a transverse wave to describe this since it is easier to see the pieces

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Anatomy of a Wave

In our wave here the dashed line represents the equilibrium position

Once the medium is disturbed, it moves away from this position and then returns to it (stadium wave analogy)

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How far up and down?

The points A and F are called the CRESTS of the wave

This is the point where the wave exhibits the maximum amount of positive or upwards displacement

crest

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How far up and down?

The points D and I are called the TROUGHS of the wave

These are the points where the wave exhibits its maximum negative or downward displacement

trough

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How far up and down?

The distance between the dashed line and point A is called the Amplitude of the wave

This is the maximum displacement the wave moves away from its equilibrium

Amplitude

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What length is it?

The distance between two consecutive similar points (moving in the same direction) is called the wavelength

This is the length of the wave pulseUse the ruler verify the wavelength definition

(start with crest to crest as shown, but investigate what other points could be used as well)

wavelength

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How long for each cycle?Period (T) = x seconds

1 cycleHow many seconds for each cycle?* You have periods in your class schedule, repeating amounts of time (82 min) for each block

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How many cycles per second?frequency (f) = 1 cycle

x secondsInverse of period in cycles/sec or Hertz

(Hz)frequency measures how often something

happens over a certain amount of time

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Relating Period and FrequencyHow many seconds for each cycle?

Period (T) = 2 sec / 1 cycleHow many cycles per second?

Frequency (f) = 1 cycle / 2 sec = 0.5 Hz

* The frequency of the classes in our schedule

is one class every 82 minutes

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Anatomy of a WaveWe know the cycle of the disturbance will

determine the parts of the waveWe know that things that repeat have a

frequency and a periodStill have questions? Watch the video to

learn more about the anatomy of a wave

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Anatomy of a WaveCheckpoint Questions

Label the anatomy of a wave (you can draw a new pulse or label what is already there)

Explain why a long cycle would result in a long wavelength and period, but could have any amplitude

What effect would this have on the frequency?

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Wave Speed

We can use what we know to determine how fast a wave is moving

What is the formula for velocity?velocity = distance / time

What distance do we know about a wavewavelength

and what time do we know about a waveperiod

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Wave Speed

so if we plug these in we getvelocity = length of pulse / time for pulse

v = / Tv = velocity (m/s)l = wavelength (m)

T = period (s)

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Wave Speed

v = / T but what does T equal?

T = 1 / fSo we can also write

v = f velocity = frequency * wavelength

This is known as the wave equation

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Wave SpeedCheckpoint Questions

Explain the effect on velocity from…Increased wavelengthIncreased periodIncreased frequencyIncreased amplitude

Recall the cycle you used to create a wave pulse. Justify which part of this cycle (and therefore which wave part) is most directly responsible for the amount of energy transferred by a wave.