VIBRATIONS AND WAVES

A wiggle in time is a vibration.

A wiggle in space and time is a wave.

A vibration can exist in one location, a wave cannot. A wave must travel from one place to another.

Vibration of a Pendulum A pendulum swings back and forth

with regularity.

The time a pendulum takes to swing back and forth depends on its length and the acceleration of gravity.

The time it takes for one back and forth swing is called a period.

The longer the pendulum is, the longer the period will be.

Our legs act like pendulums with the help of gravity.

Long legs have a slower, larger gait and short legs have a faster, shorter gait.

Wave Description The back and forth vibratory

motion of a pendulum is called simple harmonic motion.

This means that a sine curve is formed when the acceleration is proportional to the distance from equilibrium and is directed toward that equilibrium position.

A sine curve is a curve whose shape represents the crests and troughs of a wave.

The high points of a wave are called crests.

The low points are called troughs.

Measuring from the rest or home position is called the amplitude. This measurement is the maximum displacement from equilibrium.

Wavelength is the distance between identical parts of the wave, but usually we measure crest to crest.

How often a vibration occurs is called its frequency.

Frequency is measured in hertz (Hz).

One cycle per second is one hertz; two per second is 2 hertz, and so on.

High frequencies are measured in kilohertz, megahertz, or gigahertz.

AM radio is an example of kilohertz, FM radio is in megahertz, and radar and microwave ovens operate in gigahertz.

980 kHz on the AM radio causes 960,000 vibrations per second. 101MHz on FM causes 101,000,000 vibrations.

The source of all waves is something that vibrates.

Wave Motion

When energy is transferred by a wave from a vibrating source to a distance receiver, there is no transfer of matter between the two points.

The energy transferred from a vibrating source to a receiver is carried by a disturbance in a medium, not by matter moving.

Dropping a stone in a pond creates a wave, but the water is still there after the wave has passed and the water is calmed.

Wave Speed

The speed of a wave depends on the medium through which the wave moves.

The speed of sound varies depending on the medium. It is slowest through gasses, then liquids, and fastest through solids.

Wave speed, wavelength and frequency are all related.

Consider a rock concert; you do not hear the high notes before the low notes that are played in a chord.

Wave speed = wavelength x frequency

Transverse Waves

When the motion of the medium is at right angles to the direction of the wave movement, the wave is a transverse wave.

Waves in the stretched strings of musical instruments and water waves are transverse.

Electromagnetic waves are also transverse.

Longitudinal Waves

Sometimes the particles of a substance move in the same direction of a wave. The particles move along the wave.

This type of wave is longitudinal.

Sound waves are an example of longitudinal waves.

Interference

Two or more waves present in the same space create interference pattern.

Within the pattern, waves can be increased, decreased or neutralized.

When two crests overlap, they add together to increase the amplitude.

This is called constructive interference.

When one crest and one trough interact, their individual effects are reduced, or cancelled.

This is called destructive interference.

Interference occurs clearly in water, but occurs in all types of waves including sound, and light waves.

Standing Waves

A standing wave occurs when the nodes of a wave remain permanent.

The wave appears not to move.

Standing waves occur when interference occurs between a incident wave and a reflected wave.

Standing waves have nodes and antinodes.

Antinodes are the positions of greatest amplitude.

Nodes are areas of destructive interference.

Standing waves occur in both longitudinal and transverse waves.

The Doppler Effect

The change in frequency due to the motion of the source or of the receiver causes the Doppler effect.

The greater the speed of the source, the greater the Doppler effect will be.

The frequency is not actually changing; it is an apparent change that is sensed.

This effect is apparent when you hear the changing pitch of a car horn as the car passes you.

Police use this to clock your speed on the highway, except they use radar waves.

This effect also works with light.

An increase in frequency is called blue shift, and a decrease is called red shift.

This is often used in astronomy to determine the speed at which galaxies and stars are moving away or toward us.

We can also tell how fast stars are spinning, because the side spinning away shows a red shift and the side spinning toward us shows a blue shift.

Bow Waves

When the speed of the source in a medium is as great as the speed of the wave it produces, the waves pile up.

This is what happens when jets travel at the speed of sound.

Supersonic planes are faster than sound.

There is no such thing as a sound barrier. What actually happens is the plane gets harder to control as it nears the speed of sound.

A jet flying at the speed of sound flies in smooth, undisturbed air, because there are no sound waves in front of it.

The crests begin to overlap at the front edges, and the pattern made by the overlapping crests is a V-shape called a bow wave.

Bow waves are also formed when a speedboat knifes through the water faster than the wave speed.

Shock Waves

The above speedboat generates a two-dimensional bow wave.

A supersonic aircraft generates a 3-D shock wave.

A shock wave is formed from overlapping spheres that form a cone.

This cone spreads until it reaches the ground.

When it reaches the ground and passes you, you will hear the sonic boom.

Sonic booms occur the entire time a jet is traveling faster than sound.

Once an object is moving faster than sound, it will make sound after that, whether it was making sound before or not.

SOUND

The Origin of Sound

All sounds are produced by the vibrations of material objects.

This vibrating material then sends a disturbance through a surrounding medium in the form of longitudinal waves.

Under ordinary circumstances, the frequency of the vibrating source equals the frequency of sound waves produced.

The subjective frequency of sound is described by the word pitch.

A high pitch has a high vibration frequency and a low pitch has a low frequency.

A young person can usually hear pitches with 20 to 20,000 hertz.

Sound waves below 20 hertz are called infrasonic, and those that are above 20,000 are called ultrasonic. We cannot hear these pitches.

Sound in Air When sound moves through air as a

longitudinal wave, it compresses and rarefacts the air.

A pulse of compressed air is called a compression.

In between the pulses of compressed air are regions of air particles that are allowed to spread out. This disturbance is called a rarefaction.

In all wave motion, it is not the medium that moves across the room, it is the pulse, or energy that travels.

Media that Transmit Sound

Most sounds we hear are transmitted through air, but they can travel through liquids and solids also.

Solids and liquids are good conductors of sound

Sound cannot travel in a vacuum.

Sound requires a medium to travel. If there is nothing to compress and expand, there can be no sound. There can be vibration of an object, but no sound.

Speed of Sound

Sound is much slower than light.

The speed of sound in dry air at 0oC is about 330m/s. Water vapor in the air increases the speed.

Increased temperature increases speed also.

Loudness

The intensity of a sound is proportional to the square of the amplitude of a wave.

An oscilloscope measures sound intensity.

Loudness is a physiological sensation sensed by the brain. It is different in various people.

The unit for intensity of sound is the decibel. (dB)

Sound decibels increase logarithmically. Meaning, that 10dB is 10 times as intense as 0. 20 dB is 10x as intense as 10dB.

Because of this logarithmic pattern, human hearing is also logarithmic.

Forced Vibration

A forced vibration occurs when an object is forced to vibrate because of its proximity to a vibrating object.

The items that are forced to vibrate are called sounding boards.

Examples of sounding boards are guitar bodies, washtubs, and tuning fork boxes.

Natural Frequency

When any object composed of an elastic material is disturbed, it vibrates at its own special set of frequencies. This forms its own special sound.

This is called its natural frequency.

A natural frequency is one at which minimum energy is required to produce forced vibrations.

  It also requires the least amount

of energy to keep the vibration going.

Resonance

When the frequency of a forced vibration on an object matches the objects natural frequency, an increase in amplitude occurs.

This is called resonance.

Resonance means resound, or sound again.

An example of resonance is when you pump on a swing, or when someone pushes you at the right time. Your amplitude increases.

The Tacoma Narrows Bridge in WA.

Interference

Sound waves can be made to interfere.

Constructive interference makes the sounds louder.

If you move two speakers so that you receive one compression and one rarefaction at the same time, it can form a dead spot. You will still hear the sounds, but it will not sound good.

Dead spots can form in amphitheaters and gymnasiums.

Destructive noise interference is being used in anti-noise technology.

They have created noise-canceling earphones for pilots, and are working on using this technology for electronic car mufflers.

Beats

Interference occurs when two tones of slightly different frequency are sounded together.

A fluctuation of the loudness of the sounds occurs; loud then faint, loud then faint.

This is called beats.

This is similar to walking next to someone who has a different stride than you. Sometimes you are in step, and sometimes you are not.

Beats can be displayed on an oscilloscope.

To tune a piano, a tuner will use a tuning fork that matches the note correctly. When the beats disappear, he knows that the piano is in tune.

Bands can tune themselves the same way. They only need to listen to a standard note played by one instrument.