waves textbook ii

1

Sky Preece ~ 4441 Lithia Rd. ~ Buchanan, VA 24066 ~ 540-309-0840 ~ [email protected]

Student

If anything in this introduction to

waves, sound, and light

is not clear, ask questions.

Critical thought, the ability to

seek clarity and reject confusion,

is essential.

That ability can save your life,

and it could save the world.

And its noble.

Copyright 2009

Sky Amant Preece

2

Behave Wave

I saw a wave out on the sea,

Then water washed right over me.

I felt deep trembling underground,

And buildings started falling down.

Some shock, a plane passed over me,

A sonic boom, no melody.

But then a song came to my ear,

The pulse of peace and things held dear.

My mother’s shadow, then her face,

Entered my eye, and I knew grace.

You see my world is made of waves,

My life is how the waves behave.

Do you hear things? Do you see things? Do you get

your teeth X-rayed or enjoy heat or perhaps a sun tan now and then. How about television and

radio? Your life may depend on waves more than you think. Waves transfer energy from one

place to another. When that energy arrives at you, you experience it as light, sound, heat, shocks

like earthquakes and sonic booms, and movement like ocean waves.

Ocean waves, water waves, are much easier to see

than most other waves, and are a good place to start extending your understanding of the waves

in your life. Ocean or water waves also represent many of the characteristics that other waves

share. ( A wave illustration is provided on page 3.) Like other waves, water waves

exhibit:

Frequency - the number of completed wave cycles that occur in a given time. (With

ocean waves, the frequency would be how many waves break on the beach in a given time.)

Period - the time it takes to complete a wave cycle. (With ocean waves, the period would

be the time between two successive waves breaking on the beach.)

Wavelength - the distance from any point on a wave to the identical point on the next

wave. (With an ocean wave, you could mark and measure the distance between two such

points as the wave rolled along a dock or boat hull.)

Amplitude - the maximum displacement of any part of a wave from it’s equilibrium posi-

tion (at-rest position). (In an ocean wave, the amplitude would be the height or depth of its

crest or trough.)

Velocity - the speed of propagation. (usually in feet per second) (With ocean waves, you

can simply multiply a wave’s length times the frequency to find its velocity.) Try it:

The wave is 100 feet between crests, and one crest passes you every second. What is its

velocity? How many feet per second?

3

EXPLORE

Humans and wave frequencie s

EXPLORE

Detectable

by

Humans

Deep bass

Detectable

by

Humans

Screech


4

Sound waves are longitudinal waves.

Longitudinal means running lengthwise. Sound energy is conveyed by the

compression of matter along the length of the path that sound waves travel.

Sound waves are often produced by a vibrating object such as a tuning fork or

a vocal cord, but can also be produced by air that is resonating in a chamber

or an instrument like a flute. Because sound waves are conveyed by matter,

sound will not travel through a vacuum like outer space.

A slinky stretched across a table can be

made to exhibit a longitudinal wave similar to a sound wave. Compress a

section of the spiral at one end, release, and watch the compression travel the

length of the slinky. If you watch very carefully, you will not only notice the

compression as it travels, but also a decompression, or rarefaction that ac-

companies the compression. Think of the slinky spirals as air molecules and

the traveling compression as a sound wave.

In contrast, if you suspend the slinky,

and shake one end, the S-shaped wave that travels the slinky is like an ocean

wave. Energy is conveyed in the ocean by transverse waves. Transverse

means crosswise. In ocean waves the crosswise disturbance moves the water

up and down, indeed perpendicular to the direction the energy wave is travel-

ing.

Transverse

wave

(water, light)

Longitudinal

wave

(compression

wave)

(sound)

5

The speed that sound waves travel is deter-

mined by the density, temperature, and elasticity of the medium through which

they travel. Because sound relies on molecules bumping into one another to create

compressions and rarefactions, typically a sound wave will travel faster through a

more dense medium such as liquid water than in a gas like air, and even faster in a

solid like steel than in a liquid like water. The speed of sound in air, water, and

steel increases when the temperature increases. The elasticity of molecules also

helps sound go faster. Sound travels 331 meters per second in air at 0-Celcius,

366 at 100-Celcius. It travels 1482 meters per second in water at 20-Celcius, and

speeds up a full 4.6 meters per second for every one degree increase in the tem-

perature of that water. Sound travels approximately 5960 meters per second in

steel.

Humans can hear sound frequencies from 20

cycles per second to 20,000 cycles per second. Dogs hear from 20 up to 40,000

cycles per second; cats 80 up to 60,000 cycles per second. And dolphins hear

sounds from 110 cycles per second all the way up to 130,000 cycles per second.

The sensitivity to various wavelengths of energy often reflects the perception-

needs of people and animals in their environment.

Humans describe the sensation of high fre-

quency sound and low frequency sound as high pitch and low pitch. The high note

on a piano is perceived as high pitch. The low note on a bass guitar is perceived as

low pitch. Top musicians can detect frequency differences as small as two cycles

apart. Remember the human range is 20 to 20,000 cycles per second; now that’s

discernment.

Longitudinal waves, such as sound waves,

and transverse waves, such as ocean waves, can be studied using musical instru-

ments. Longitudinal sound waves are what people think of first with musical in-

struments, but transverse waves in the strings, reeds, drumheads, and sound boards

also play an important part in producing musical sounds.

Resonance is another important wave charac-

teristic, and it is essential to most musical instruments. Resonance is the natural

frequency at which things vibrate or oscillate. On a guitar, the strings resonate at

various frequencies depending on the length and weight of the strings. The same

is true of a piano. With a flute or trombone the air inside the instrument resonates

at various frequencies depending on the length of the column of air in the instru-

ment. The same natural frequency response, or resonance, can be heard from the

air inside a pop bottle if you supply energy by blowing across the opening, and

you can change the natural frequency by drinking pop from, or adding pop to, the

bottle. The design of an instrument affects how these vibrations or oscillations are

transmitted into the air and subsequently to your ear.

6

Wave Features

sound

oscilloscope


7

Everything you see is light. Whether it is light

originating from a source like the sun, or reflected off an object like a pencil or your

house, light is what you get to know visually about the world. You don’t see things, you

see light from things.

Light waves are part of the electromagnetic spec-

trum and do not require matter as a medium through which to travel as sound waves do.

Light waves are transverse waves. Transverse means crosswise. Much like ocean waves,

light waves cause a crosswise, or perpendicular, disturbance in the electromagnetic field

through which they travel. Other waves that are electromagnetic are radio, television, ra-

dar, x-rays, and cosmic rays. Light waves are the only part of this broad spectrum of elec-

tromagnetic waves that can be seen by humans.

Visible light is perceived by humans as colors

ranging from red to violet. Light waves perceived as red have a lower frequency than

light waves perceived as blue. As you might guess, the higher the frequency, the higher

the energy. In the same way you would receive more energy if you were slammed by 100

ocean waves per minute than if you are hit by one ocean wave per minute, higher fre-

quency blue light delivers more energy than lower frequency red light. And ultraviolet, an

even higher frequency light wave, can burn your skin. Watch out for the sun burn.

8

Light waves travel much faster than

sound waves. While sound is traveling along at about one mile every five

seconds, light rips along at about 18,600 miles every tenth of a second.

That’s about 900,000 times faster. That’s why you see lightning before you

hear thunder. The speed of light in a vacuum is 186,000 miles per second.

The speed of light is reduced slightly

when it enters earth’s atmosphere, and then is reduced dramatically when it

enters a denser medium like water or glass. The speed of light in glass is only

two thirds the speed of light in a vacuum.

When light waves pass from one me-

dium, like air, into another medium, like glass, they bend. This deviation

from light’s straight path is called refraction. This effect can be observed

twice when light, which appears white because it contains all the colors of the

spectrum, passes through a prism. Refraction happens once when light enters

the prism, and once when it exits.

The evidence of refraction can also be

seen in a rainbow where rain drops refract light. As you might guess, rain

drops also reflect light. Notice that the source of rainbow light, the sun, is

always behind you, and the rainbow is in front of you.

Reflection of light in the raindrop or the

reflection you see in a mirror demonstrate a characteristic of all waveforms.

The reflection of sound is what you hear in an echo. The reflection of an

ocean wave off a cliff sends the wave back out to sea. Reflected light is what

you see when you look at any object or thing that does not create light itself.

Most objects you look at absorb some

of the many colors from the light that illuminates them, and reflect other col-

ors. The color an object reflects is the color you identify with that object.

Oddly, that object has converted the other light wave frequencies, the colors

you don’t see, into heat, momentum, or electricity.

Prism Rain Drop

9

The lens of your eye is transparent, Like

glass or air. Images pass through such material clearly. The lens of your eye also

refracts the light that passes through it, focusing the image on the retina at the back

of your eyeball.

Other parts of your body are translucent.

Translucent materials allow some light to pass through but clear images cannot be

seen. A bright flashlight will shine through your cheek, hand, or earlobe, but the

light that comes through is a glow, not an image. Wax paper and frosted glass are

translucent.

Opaque material allows no light to pass

through it. Aluminum foil, most concrete, and the thick parts of your body are

opaque to visible light. Your body is not opaque to x-rays, however. X-rays shine

right through you. Your house walls are opaque to visible light, but transparent to

radio waves and microwaves.

Light waves and sound waves radiate from

their sources in many directions. Because the wave energy spreads out as it travels

away from its source, it’s intensity drops rapidly. In fact, whatever the energy inten-

sity is at say one foot away, the intensity would be one-fourth of that at two feet, one

-ninth of that at three feet, and so on. (This progression is an inverse-square ratio.)

You were probably familiar with the Dop-

pler Effect before you entered school. Try imitating the sound of a car racing to-

ward you, and then tearing off toward the horizon. That’s the Doppler Effect. All

waves exhibit it. When a wave source for sound, light, and other waves is coming

toward you the frequency you hear gets higher. When the source is moving away

the frequency you hear diminishes. That’s how the police detect you speeding. It’s

how Doppler radar helps the weather man determine the speed of storm systems.

Red shifted light, shifted toward a lower frequency, helps astronomers identify stars

racing away from us, and blue shifted light, shifted toward a higher frequency, re-

veals a star heading toward us. A doctor might use a Doppler Ultrasound to check

up on your soon to be born baby brother or sister. Waves matter.

Inverse– square Intensity The Doppler Effect

10

Wave ef fects

Refraction

Reflection

Doppler Effect

Interference

Polarization


11

Wave Exper iments

1. Oatmeal Box and Candle: compression wave, shock wave, medium

displacement.

2. Whip: transverse wave, conservation of energy, shock wave, (sonic

boom like a plane).

3. Slinky: natural frequency, resonance, harmonics, transverse wave,

longitudinal or compression wave.

4. Tuning Forks: natural frequency, sympathetic resonance, trans-

verse wave, compression wave, Doppler effect.

5. Prism: refraction, how a lens works, wavelength, electromagnetic

waves.

6. Polarizing Lens: polarization, scattering, reflection, electromagnetic

waves.

7. Musical instruments (guitar and flute): transverse waves, com-

pression waves, wavelength, frequency.


12

Waves def ined

Longitudinal wave: energy transmission where particles

oscillate back and forth around a center along a line in

the direction the wave is moving. (compression wave,

sound, shock wave)

Transverse wave: energy transmission where individual

particles move perpendicular to the direction of the ad-

vancing wave. (water wave or light)

Frequency: the number of completed waves or cycles

that occur in a given time. (Hertz, Hz is cycles per second.)

Period: time it takes for one complete wave oscillation to

occur.

Wavelength: distance from any point on a wave to an

identical point on the next wave.

Amplitude: maximum displacement of any part of a

wave from its equilibrium position. (crest or trough)

Velocity: speed of propagation (feet per second).

Wave Velocity: is equal to the wavelength times the frequency.

Wave Velocity: is also equal to wavelength divided by

the period.


13

Wave Talk and Learning Experience

This learning experience that introduces students to wave physics, espe-

cially sound and light, is designed to meet the time limit of less than one hour.

That’s asking a lot. So it is also designed to be expandable. Each step can be

lengthened and given more time, thereby allowing students to explore more ex-

perimental activities, ask more questions, discuss more ideas, and generally to be

more inspired.

Here is the recommended sequence:

(1) After a short introduction, show the five minute DVD Just

Wave, a palisade of images, ideas, terms, concepts, and cu-

riosities concerning wave physics, designed to engage stu-

dents. Discuss.

(2) Have the students participate in Wave Experiments, a col-

lection of hands on activities that enable the students to

explore and experience wave effects in a hands on way.

Initiative and open discussion should be encouraged.

(3) Show Just Wave again, only without sound, and pausing

at any engaging frame to ask students questions and

continue discussion. Basic definitions, concepts, and

ideas should be discussed and expanded with students.

(4) Wave Thinking pages support explanation, student

understanding, and further discussion and learning.

Wave Learning experi ence


waves textbook ii

Documents

ocean waves

longitudinal waves

waves break

successive waves

waves share

sound waves travel

water waves exhibit

waves transfer energy