A wave is a wave is a wave

An introduction to waves

What are some types of waves?

• Water

• Sound

• Light

• Matter

• Sports fans

• Earthquakes/seismological

• Hand?

What distinguishes waves?

• Water, Sound, Light, Sports Fans, quakes

• Information moves without individual particles carrying it

What is a wave? - Webster says...

• a moving ridge or swell [on a surface of water]• a swell, surge, or rush• any surging or progressive movement resembling

a wave of the sea• Physics. a progressive disturbance propagated

from point to point in a medium or space without progress or advance by the points themselves

What is a wave? - Dr. DJ says

• the method of transmitting information/energy/etc. from point A to point B without individual objects traveling between the points

Transverse waves• Water wave: water moves up and down,

wave moves toward shore• Rope: string moves up and down, wave

moves toward end• Sports fans: fans rise and sit, wave moves

around stadium• Electromagnetic (light): fields vary in a

direction perpendicular to motion

Longitudinal waves

• Slinky: Coils compressed and released create wave in direction of compression

• Sound: Air compresses in direction of motion, but molecules don’t travel from source to ear

The sinusoidal (in space) “wave”

• One wavelength occupies 2 radians

• Described by

A=Amaxcos(2x/)

A

x

A

A=Amaxsin(2x/)

A

A=Amaxcos(2x/)

A

A=Amaxsin(2x/)

The sinusoidal (in time) “wave”

• A cycle completes in one “period,” which occupies 2 radians

• Described by

A=Amaxcos(2t/T+)

A=Amaxsin(2t/T +)

A

t

T

Wave vocabulary• wavelength = distance per cycle• wave number k = radians per distance

2/ = rad/cycle (cycle/m) = rad/m = k• period T = time per cycle• angular frequency = radians per second

2/T = rad/cycle (cycle/s) = rad/s = • frequency f = number of cycles per second

f = cycles/second = 1/(second/cycles) = 1/T• Speed v = distance per time; wave travels in T

v = /T

The traveling wave• A wave varies in both space and time:

– At one location, the amplitude varies in time– At one time, the amplitude varies in space

• A sinusoidal wave moving toward positive x is described by

A = Amaxcos(kx – t + ) • A sinusoidal wave moving toward negative x is

described by

A = Amaxcos(kx + t + )

Animation of traveling waves

Do the Before You Start part of the activity

Think about the questions by yourself for ~5 minutes, then work with your assigned group to answer the questions. You should finish in

about 15 more minutes.

Each group member should fill out his or her own activity sheet.

Do We All Agree?

• What is the frequency of the wave?• How can we sketch a graph of the wave without

resorting to graphing calculators/software?• How does this graph change when we change the

phase constant?• What are the differences between a graph of V vs.

t and a graph of V vs. x?

Do the rest of the activity

Your instructor will point out a few features of the equipment. After this has been done, work

with your assigned group to complete the activity. You should finish in ~40 minutes.

What have we learned today?• Waves transmit information between two points without

individual particles moving between those points

• Transverse Waves oscillate perpendicularly to the direction of motion

• Longitudinal Waves oscillate in the same direction as the motion

• The spatial dependence of periodic waves can be described by either the wavelength or the wave number k, which are related.

• The time dependence of periodic waves can be described by either the period T, the angular speed , or the frequency f, which are all related.

What else have we learned today?

• Any traveling sinusoidal wave may be described by

y = ym sin(kx t + )

is the phase constant that determines where the wave starts.

Before the next class, . . .

• Read the Assignment on Waves found on WebCT

• Read the Assignment on Reflection and Refraction using on-line tutorial (start from WebCT Contents)

• Do Reading Quiz 1 which will be posted on WebCT by Tuesday.