harmonic motion and waves 3.3.2015arsenie. harmonic motion is motion that has a pattern or...

Harmonic Motion and Harmonic Motion and WavesWaves

3.3.2015 3.3.2015

ArsenieArsenie

Harmonic motion is Harmonic motion is motion that has a motion that has a pattern or pattern or repetition. This repetition. This type of motion is type of motion is called called oscillation.oscillation.

Things that oscillate have a cycle. We Things that oscillate have a cycle. We measure several things about a cycle. measure several things about a cycle.

Period (Period (TT) is the time it takes for one cycle to ) is the time it takes for one cycle to complete. It is measured in seconds. complete. It is measured in seconds.

Frequency ( Frequency ( f f ) is the number of cycles that occur in ) is the number of cycles that occur in one second. It is measured in Hertz (Hz). 1 cycle per one second. It is measured in Hertz (Hz). 1 cycle per second = 1 Hz. second = 1 Hz. 1 million cycles per second = 1,000,000 Hz = 1MHz.1 million cycles per second = 1,000,000 Hz = 1MHz.

Amplitude (Amplitude (AA) is the size of the cycle away from its ) is the size of the cycle away from its center of equilibrium/rest. We measurethe distance center of equilibrium/rest. We measurethe distance in meters or an angle in degrees.in meters or an angle in degrees.

AmplitudeAmplitude Amplitude measures the Amplitude measures the ““greatnessgreatness”” of a of a

wave, or the maximum height from the wave, or the maximum height from the center. Units can be in m or the angle.center. Units can be in m or the angle.

Example: a pendulumExample: a pendulum’’s amplitude of 20 s amplitude of 20 cm, or 30cm, or 30°°

A A wavewave is is an an oscillation oscillation that travels.that travels.

Waves carry useful Waves carry useful information and energy.information and energy.

Waves are all around Waves are all around us:us: light from the stoplightlight from the stoplight ripples in a puddle ripples in a puddle electricity flowing in electricity flowing in

wireswires radio and television and radio and television and

cell phone transmissionscell phone transmissions

Anytime you see a vibration that moves...Anytime you see a vibration that moves...

Anything that makes or responds to sound... Anything that makes or responds to sound...

Anything that makes or responds to light ...Anything that makes or responds to light ...

Anything that transmits information through Anything that transmits information through the air (or space) without wires...the air (or space) without wires... cell phones, radio, televisioncell phones, radio, television

Anything that allows you to Anything that allows you to ““see throughsee through”” objects...objects... ultrasound, CAT scans, MRI scans, and X raysultrasound, CAT scans, MRI scans, and X rays

Waves have cycles, frequency, and amplitude, because they Waves have cycles, frequency, and amplitude, because they are oscillations.are oscillations.

The frequency of a wave tells how often each point oscillates.

The amplitude of a wave is the maximum movement from equilibrium.

The wavelength (λ) of a wave is the length of one complete cycle.

It is measured in meters.

Crest

Trough

The The speedspeed of a wave equals the of a wave equals the frequency times the wavelength.frequency times the wavelength.

v = f

Frequency (Hz)

Wavelength (m)

Speed (m/sec)

A very important and confusing note:A very important and confusing note: The speed of a wave will not change if you The speed of a wave will not change if you

increase the period. The reason is this: increase the period. The reason is this: if you increase the time, you are actually stretching the if you increase the time, you are actually stretching the

wave out. You see time as a larger number, but: wave out. You see time as a larger number, but: This will decrease the frequency proportionally (less of it will This will decrease the frequency proportionally (less of it will

happen in 1 second). happen in 1 second). That also means the wavelength had to increase proportionally That also means the wavelength had to increase proportionally

(stretch out farther). (stretch out farther). So if the period is increased, So if the period is increased, the frequency is decreased by the same amount, the frequency is decreased by the same amount, and the wavelength is increased by the same and the wavelength is increased by the same

amount,amount, which means that the speed ( which means that the speed ( ff xx λλ )) will STAY will STAY

THE SAME number as it was before. THE SAME number as it was before. EVERYTHING IS PROPORTIONALEVERYTHING IS PROPORTIONAL

WAVE SPEED IS ONLY DEPENDENT ON THE WAVE SPEED IS ONLY DEPENDENT ON THE MEDIUM IT IS TRAVELING THROUGH. MEDIUM IT IS TRAVELING THROUGH. This means that whatever kind of wave it is, it will This means that whatever kind of wave it is, it will

indefinitely travel at the indefinitely travel at the same speedsame speed, no matter , no matter the change in frequency, wavelength, period, etc. the change in frequency, wavelength, period, etc.

It will only change speed when it passes through a It will only change speed when it passes through a different medium (water, air, oil, pudding, applesauce, different medium (water, air, oil, pudding, applesauce, etc). etc).

When you tighten a guitar string, you change the When you tighten a guitar string, you change the tension. This counts as changing the medium. tension. This counts as changing the medium.

Transverse waves:Transverse waves: these oscillate perpendicularly to the direction of the wave.

The wave moves left to right, but the oscillation is up and down. The wave moves left to right, but the oscillation is up and down. Water, light, electricityWater, light, electricity

Longitudinal WavesLongitudinal Waves These oscillate These oscillate parallelparallel to the wave direction. to the wave direction.

springs stretching and compressing (slinkies), soundsprings stretching and compressing (slinkies), sound

Wave interactionsWave interactions

Wave is absorbed by a material and energy is

transferred (lose amplitude)

The material a wave The material a wave interacts with is called a interacts with is called a boundaryboundary. .

The wave approaching a The wave approaching a boundary is called the boundary is called the incident waveincident wave. .

The wave sent from a The wave sent from a boundary is the boundary is the reflectedreflected wave. wave.

A wave that is bent A wave that is bent passing through a passing through a boundary is called a boundary is called a refracted waverefracted wave..

This incident plane wave refracts a circular wave after passing through a convex barrier.

Waves Waves add up add up when they cross each other. when they cross each other. Two pulses traveling towards each other combine into a

resultant pulse.

=

Waves will pass each other and keep Waves will pass each other and keep going…going…

After they pass…