WAVES

A wave is a disturbance that carries energy through matter or space.

The matter through which a wave travels is called a medium.• For waves in a lake, water is the medium.• For sound from a television, air is the medium.• For earthquakes, the earth is the medium.

Waves that require a medium are called mechanical waves. – Mechanical waves CANNOT travel through a vacuum.

Electromagnetic waves consist of oscillating electric and magnetic fields, which radiate outward at the speed of light.– Do not require a medium

Types of electromagnetic waves: Radio waves Microwaves Infrared Visible light Ultraviolet (UV) X-rays Gamma rays

Recall that energy is the ability to do work, or to exert a force over a distance. Waves transfer energy.

The larger a wave is, the more energy it carries.

Tsunami waves are created by underwater disturbances such as earthquakes, volcanic eruptions, and underwater landslides. These waves harness a great amount of energy and are very dangerous.

Energy may spread out as a wave travels.

Each of the circles in the wave above is called a wave front. They each carry the same amount of energy, but in the larger circles, this energy is spread out over a greater distance. Mechanical waves spread out spherically from the source, if the source is open to the medium in all directions.

Most waves are caused by vibrations. Vibration: in a general sense, anything that switches back

and forth, to and fro, side to side, in and out, off and on, or up and down is vibrating.

Only the energy travels in the wave, not the medium. The medium only vibrates around its equilibrium position.

Holt Science Spectrum: Physical Science

The image above displays the energy changes as a mass on a spring vibrates around its equilibrium position.

This photo and the animation on the previous slide are examples of simple harmonic motion.

Holt Science Spectrum: Physical Science

Transverse waves are waves in which the motion of the particles is perpendicular to the direction the wave is traveling.

Longitudinal waves are waves in which the particles of the medium vibrate parallel to the direction of the wave motion.

Rarefaction Compression

Crest

Trough

Mechanical waves– Can be transverse or longitudinal

Electromagnetic waves– transverse

Particles in a surface wave move both perpendicular and parallel to the direction in which the wave travels. These waves occur at the boundary of two different media, such as water and air.

Wave Properties• The amplitude of a wave measures the amount of

particle vibration.amplitude: the maximum distance that the particles of a wave’s

medium vibrate from their rest position– for a transverse wave, measured from the rest position to the

crest or the trough– expressed in the SI unit meters (m)– Ideal transverse waves are shaped as sine curves.

wavelength: the distance from any point on a wave to an identical point on the next wave– for a transverse wave, measured from crest to crest or trough to

trough– for a longitudinal wave, the distance between two compressions– represented by the Greek letter lambda, l– expressed in the SI unit meters (m)

Amplitude and wavelength tell you about energy.

larger amplitude = more energy

shorter wavelength = more energy

Frequency is a measurement of the vibration rate.

frequency: the number of cycles or vibrations per second; also the number of waves produced in a second.

– represented by the symbol f– expressed in the SI unit hertz (Hz), which equals 1/s

Example:Suppose I wiggle a slinky back and forth, and count that 6

waves pass a point in 2 seconds. What would the frequency be?

– 6 cycles / 2 seconds = 3 cycles / 1 second– 3 Hz

Period: in physics, the time that it takes for one full wavelength to pass a given point.

– represented by the symbol T– expressed in the SI unit seconds (s)

The period of a wave is related to the frequency by the following equation:

T = 1 or f = 1 f T

Period of wave (a) Period of wave (b)T = 1/4Hz = 0.25s T = 1/8Hz = 0.125s

Wave Speed• Wave speed equals wavelength divided by

period.speed = distance/time

• Wave speed equals frequency times wavelength.

v = l T

v = f l

Wave Speed The string of a piano that produces the note middle C vibrates with a frequency of 262 Hz. If the sound waves produced by this string have a wavelength in air of 1.30 m, what is the speed of the sound waves?

Given: frequency, f = 262 Hz wavelength, = 1.30 m

Unknown: wave speed, v = ? m/s

v = f

v = 262 Hz 1.30 m

v = 341 m/s

• The speed of a wave depends on the medium.– In general (for mechanical waves), wave speed is

greatest in solids and least in gases. – In a given medium, the speed of waves is constant.

• Shaking your hand faster while holding a rope will not increase the wave speed along the rope. It simply increases the frequency and decreases the wavelength.

Kinetic theory explains differences in wave speed.• In gases, molecules are farther apart. They

need to travel through more empty space before hitting another molecule than they would in liquids and solids.

• Light has a finite speed.– the speed of light in empty space (c) = 3.00 108 m/s

(186,000 miles per second)– for electromagnetic waves, c = f l

Electromagnetic waves travel fastest in a vacuum and slower through mediums such as air or water.

Why does the pitch of an ambulance siren change as the ambulance rushes past you?

〉Motion between the source of waves and the observer creates a change in observed frequency.

• Pitch is determined by the frequency of sound waves.

• The pitch of a sound (how high or low it is) is determined by the frequency at which sound waves strike the eardrum in your ear.

• A higher-pitched sound is caused by sound waves of higher frequency.

• Frequency changes when the source of waves is moving.

– Doppler effect: an observed change in the frequency of a wave when the source or observer is moving

– The Doppler effect occurs for many types of waves, including sound waves and light waves.

Stationary wave source. The sound waves move symmetrically out from the source.

Moving wave source. Since the source of the sound is moving to the right, the wavefronts seem to bunch up to the right and spread out toward the left. This causes the observed pitch to be different depending on where the source is in relation to the observer.

This is an illustration of an object moving with a speed that is equal to the speed of sound.

(Mach 1)An observer in front of the object

would not hear anything until the object arrived.

An F/A-18 Hornet creating a vapor cone at transonic speed just before reaching the speed of sound

http://www.acs.psu.edu/drussell/Demos/doppler/mach1.html

This animation is an example of an object moving faster than the speed of sound.

The image above shows a sonic boom created by the THRUST SSC team car as it broke the land speed record and the sound barrier.

An observer will hear the sonic boom from an object moving faster than the speed of sound when the shock wave, on the edges of the cone, crosses his or her location.

Wave InteractionsHow do waves behave when they hit a boundary, when

they pass around an edge or opening, and when they pass from one medium to another?

〉When a wave meets a surface or a boundary, the wave bounces back.

〉When a wave passes the edge of an object or passes through an opening, the wave bends.

〉 A wave also bends when it passes from one medium to another at an angle.

Reflection occurs when a wave meets a boundary.

– reflection: the bouncing back of a wave when it hits a surface that it does not go through

Examples: – The reflection of light waves in a lake can create a

mirror image of a landscape. – Water waves are reflected when they hit the side of

a boat.

The animation below shows a wave pulse on a string being reflected off of a fixed boundary. The wave exerts an upward force on the end of the string. But, since the end is clamped, it cannot move. According to Newton's third law, the wall must be exerting an equal downward force on the end of the string. This new force creates a wave pulse that propagates from right to left, with the same speed and amplitude as the incident wave, but with opposite polarity (upside down).

The wave in the animation below is traveling from a lower density to higher density medium.

This wave is traveling from a higher to lower density medium.

Diffraction is the bending of waves around an edge.

– diffraction: a change in the direction of a wave when the wave finds an obstacle or an edge, such as an opening

Examples: – Water waves

diffract around a block in a tank of water.

– Sound waves passing through a door diffract.

Waves can also bend by refraction.

refraction: the bending of a wavefront as the wavefront passes between two substances in which the speed of the wave differs

All waves are refracted when they pass from one medium to another at an angle.

interference: the combination of two or more waves that results in a single wave

• Constructive interference increases amplitude.– constructive interference: a superposition of two or more

waves that produces an intensity equal to the sum of the intensities of the individual waves

• Destructive interference decreases amplitude.– destructive interference: a superposition of two or more

waves that produce an intensity equal to the difference of the intensities of the individual waves

http://serc.carleton.edu/NAGTWorkshops/deepearth/activities/40826.html

Standing wavesOccurs when a wave reflects upon itself and interference causes

the pattern

Each loop of a standing wave is separated from the next loop by points that have no vibration, called nodes.

Midway between the nodes lie points of maximum vibration, called antinodes.