A Description of the Phenomenon of Energy Movement OR

Periodic Motion & VIBRATIONSaka

Simple Harmonic Motion

Simple harmonic motion periodic motion where the unbalanced force varies directly with the displacement from the equilibrium point; this motion is described by the period, the frequency, and the amplitude of the motion – example: A Pendulum

Period (T)the time in seconds needed to complete one cycle of motion Amplitude the distance from the equilibrium point to the point of greatest displacement

frequencythe number of vibrations in a time interval; its SI

unit is hertz (Hz)

I like to use the Greek letter, f , as the symbol for frequency. This can be confusing to students since

its appearance is similar to the letter f .

1 Hz = 1 sec-1 T = 1/ or T = 1/f

Waves and Vibrations

Wave Motion

Waves transport energy, not particles.

Imagine a fishing bobber floating on top of the water. As water waves pass, the bobber may move

up and down, but it stays in the same horizontal location.

BASIC WAVE CLASSIFICATIONS•1. MECHANICAL WAVES -• type of energy transfer involving some

sort of medium - matter through which

the wave energy moves.

• The wave energy causes the particles to move or vibrate, but not move along with the wave itself.

• EX: water, sound, earthquake waves

•2. ELECTROMAGNETIC WAVES - • This type of waves does not need any

matter medium to travel through - travels at the speed of light. These waves are defined as periodic disturbances of an electromagnetic field.

Notice the wide variety of waves in the EM spectrum!

HOW DO WAVES MOVE?TRANSVERSE - this wave type vibrates the particles or field through which they pass at right angles to the direction of wave motion.

Ex: water waves, waves in a rope...

http://www.colorado.edu/physics/phet/simulations/stringwave/stringWave.swf

http://www.acoustics.salford.ac.uk/feschools/waves/trans

LONGITUDINAL - this wave type vibrates the particles or field through which they pass parallel to the direction of wave motion.

Ex: sound waves

http://www.acoustics.salford.ac.uk/feschools/waves/wavetypes2.htm

http://www.smgaels.org/physics/home/animations3/waves/wavemotion.html

WAVE PARTS/CHARACTERISTICS• Crest - top of wave • Trough - bottom of wave

Wavelength - distance between 2 successive crests or troughs symbol = Wave Fronts - a locus of adjacent points that are in phase

Amplitude - maximum height or depth of wave from midpoint -also a measure of the amount of work a wave can do or its ENERGY

Frequency - the number of waves that pass a fixed point in a given amount of time - usually per second - # of waves or cycles/s = HERTZ - kHz - 1000 Hz mHz - 1 X 106 Hz

Wave Period - the amount of time it takes for 1

complete cycle to pass a fixed point.

T = 1 / f

1. The wavelength of the wave is ______.2. The amplitude of the wave is _____.

Wave SpeedGeneric wave speed formula that holds true for all

types of waves:

wave speed = wavelength x frequency

v = λ f

λ = Greek letter “lambda”, represents wavelength.

http://www.users.globalnet.co.uk/~bunce/sound.htm#cause

An Example:You may have used a 900 MHz cordless phone.

These waves travel at the speed of light, 3 x 108 m/s. What is the period and wavelength of these cordless

phone waves?

To get the period:

T = 1/f

T = 1/ (9 x 108 Hz)

T =1.1 x 10-9 sec

To get the wavelength:

v = 3 x 108 m/s ; f = 9 x108 Hz

v = λ f

3 x 108 m/s = λ (9 x108 Hz)

λ = .33 m

WAVES QUIZ1. LABEL ALL CRESTS & TROUGHS2. USE YOUR RULER TO DETERMINE THE AMPLITUDE AND WAVELENGTH.3. HOW MANY WAVELENGTHS ARE REPRESENTED IN THIS DIAGRAM?

Waves Quiz1. If it takes 10 s for the wave to reach point A:a.)What is the Wavelength?b.)What is the Amplitude? c.)What is the Frequency? d.)What is the Period? e.)What is the Wave Speed?

Waves Quiz1. What are the differences/similarities between:a.) Mechanical vs. Electromagnetic Waves

b.) Transverse vs. Longitudinal waves

• The Dynamics of the Motion of Sound Energy through Matter

• Sound waves are longitudinal waves produced by variations in air pressure.

Longitudinal wave

• The energy of a sound wave travels away from the source through a series of molecule collisions parallel to the direction of the wave.

Tuning fork

http://www.users.globalnet.co.uk/~bunce/sound.htm#cause

Sound does not consist of air moving towards us in bulk; BUT A WAVE OF ENERGY CAUSING THE MOLECULES OF AIR TO VIBRATE - TRANSFERRING ENERGY

http://www.users.globalnet.co.uk/~bunce/sound.htm#cause

This is what you would see on an oscilloscope!!

Speed of Sound:Although we usually use 343 m/s for the speed

of sound, this number varies because of a variety of factors. Note: check your reference

tables!

Wind, temperature, and humidity are all factors that influence the speed of sound.

343 m/s is for 20oC and 1 atmosphere.

Other Media:Sound does not only travel in air. In fact, sound

travels faster through most solids or liquids compared to air. The collisions travel better in

more dense media.

H2O molecules more tightly packed

Gas molecules less tightly packed

• SOUND TRAVELS @ Approx 340 m/s (at rm temp) - IN AIR!

• At normal atmospheric pressure, the temperature dependence of the speed of a sound wave through air is approximated by the following equation:

• v = 331 m/s + (0.6 m/s/C)*T

• Sound waves can also travel through liquids and solids.

• SOUND TRAVELS in water is 1480 m/s or 4856 ft/s. - More than 3000 miles per hour.

• Velocity of sound varies as the inverse of the square root of the density of the medium it is in. The speed also then will depend on the temperature of the medium too. For steel is it about 4870 m/sec.

• Unlike light, sounds needs some kind of material to propogate through. In a vacuum there is nothing, so sound cannot go through a vacuum.

Measuring sound waves

• The frequency of a sound wave is called pitch.

• The human ear is able to feel frequencies between 20 Hz to 20,000 Hz, depending on the age of the person.

• The amplitude or volume of a sound wave is the amount of pressure exerted by a sound source to air molecules.

• The pressure is measured by the intensity of the sound. In dB’s or decibels!!

• Decibel chart

Pitch:

Pitch is equivalent to frequency.

high pitch = high frequency

low pitch = low frequency

1000 Hz 1500 Hz 2000 Hz

Human Hearing:Most humans hear approximately 20Hz through 20,000 Hz. Although this may diminish with age.

The Animals: As you may know, many animals have higher or lower ranges to their hearing compared

to humans.

Beyond the Limits:

Sounds of a higher frequency than we can hear are called ultrasonic. ( ultraviolet is

higher frequency than violet light)

Sounds of a lower frequency than we can hear are called infrasonic. (infrared is lower

frequency than red light)

Nature of Sound in Air:

Sound is simply a longitudinal wave carrying energy that our ears detect.

Reflection of Sound:

When sound reflects off a surface, we call it an echo.

Animal Reflections:Bats and dolphins emit sound that is reflected off objects. The reflected sound is received by them

and allows them to “see” their environment.

Reverberations:When many sounds echo many times off multiple

surfaces, that is called a reverberation.

You might get this in a large hall that

has no sound dampening.

Refraction of Sound:

Since sound travels at different speeds in various temperatures of air, sound can bend if there is a

layer of different temperature air.

Sometimes at night you can hear very distant objects...

Tuning Forks:

A tuning fork provides a continuous push or vibration that creates a particular frequency.

Although you may not be able to see it, the tines actually do move back and forth.

As you may have noticed, the length of the tuning fork helps determine the frequency of its vibration.

Natural Frequency:Any elastic material object will vibrate at one particular natural

frequency.

When you lightly tap a crystal glass, you hear its natural frequency.

When an object is forced to vibrate, and this vibration matches its natural frequency, you have resonance.

It is constructive interference since the repeating waves of the natural frequency add up to produce a larger wave.

Swing Analogy:Imagine starting to push someone on a swing. You need to push them at just the right time, so that their amplitude continually increases.

A certain bridge was unlucky enough to have its natural frequency match the wind frequency at that location. These wind waves constructively interfered and produced a large enough wave to completely destroy the bridge!

Closed Tubes:

With a closed tube, resonance occurs at only certain lengths:

odd 1/4 multiples of λ

Note: a node at closed end, antinode

at the open end.1/4 λ

3/4 λ

5/4 λ

Also called - CONSTRUCTIVE INTERFERENCE

Also called - DESTRUCTIVE INTERFERENCE

Beats:A strange effect happens when you add waves that

are just slightly different frequencies.

You get beats, a periodic variation in amplitude.

The two top waves add together,

superimpose, to produce the

bottom pattern...

Doppler Effect

A stationary source of waves would produce concentric wave circles:

A moving source would create waves that are centered closer to the direction of movement.

The Doppler effect is a shift in frequency due to a moving source or receiver.

It is often observed as a car horn, or siren passes you.

Police use the doppler effect to detect speeders. When the waves bounce off the oncoming car, its frequency is shifted. This is used to calculate a

speed.

Astronomers use the doppler shift of light from distant galaxies to learn about their motions.

Objects that are moving towards the observer are said to be blue shifted.

blue = higher frequency.

Objects that are receding are said to be red shifted.

red = lower frequency.

Shock Waves:As a source of waves nears the actual speed of the

waves it produces, those waves “pile up”.

The “V” shape of these overlapping waves is called a bow wave.

Sonic Boom:When an airplane flies faster than sound, a

continuous loud rumbling is created (sonic boom).

Other examples of sonic booms include a cracking whip, and a supersonic bullet.

A 20mm shell flying at 500 m/s. Notice the shock waves produced.

The exposure was only 20 nanoseconds!