Waves

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C.

NOTES 1
-

Topic 4
-

Waves*

-------------------------------------------------------------------------------------------------

There are two different categories of waves...


A. Waves that don’t require a medium
-

Electromagnetic Waves
;


B. Waves that do require a medium
-

Mechanical Waves
;


4.4.9

Electromagnetic Waves (aka EMR...electromagnetic radiation)


Electromagnetic Waves

-

oscillating electric/magnetic fields which all
travel at 3.00 x 108 ms
-
1, transmit energy, but do not require a physical

medium (ie., they can travel through a vacuum);



*Heat..................... f < 1 x 102 Hz ............ l > 1 x 104 m


Radio................... f ª 1 x 104 Hz ............ l ª 1 x 103 m


*TV........................ f ª 1 x 105 Hz ............ l ª 1 x 102 m


Microwaves.......... f ª 1 x 108 Hz ............ l ª 1 x 10
-
2 m


Infrared Light........ f ª 1 x 1012 Hz .......... l ª 1 x 10
-
5 m


Visible Light.......... f ª 1 x 1014 Hz .......... l ª 1 x 10
-
6 m


Ultraviolet Light..... f ª 1 x 1016 Hz .......... l ª 1 x 10
-
8 m


X
-
rays................... f ª 1 x 1018 Hz .......... l ª 1 x 10
-
10 m


Gamma Rays....... f ª 1 x 1020 Hz ........... l ª 1 x 10
-
12 m


[*Not on chart...nobody’s perfect!!]

4.4.1

Mechanical Wave Pulse versus a
Continuous Traveling Mechanical Wave




wave pulse

-

work is done on a medium once;
one “disturbance” moves through a medium;



continuous traveling wave

(
periodic wave
)

-

work done on a medium in a continuous,
periodic manner; multiple wave pulses are
generated; periodic “energy disturbances” move
through a medium;



4.4.2 Mechanical Waves...transfer
energy, not matter



1. Work is done on a medium
-

the molecules of the medium, depending
on phase (solid, liquid, gas) and type (element, compound, mixture),
move/vibrate, according to the limits of their binding energies;


2. Gas molecules vibrate a great distance compared to their size;
atoms in a solid vibrate a small distance compared to their size;


3. The vibrating molecules collide with adjacent molecules and
transfer the kinetic energy (KE = energy of motion) of the molecules to
adjacent molecules;


4. These molecules begin vibrating, colliding, transferring KE, and so
on;


Energy is transmitted through the medium but the molecules do not
move very far from their original position. The medium, itself, does not
move!!




Wave Basics

I

http://aspire.cosmic
-
ray.org/labs/waves/wave_basics/waves.htm




Wave Basics II

http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html



Mechanical Wave

-

vibrating molecules/atoms transmit energy but not matter through a
physical medium;


4.4.3
Mechanical Waves...Transverse
and Longitudinal Waves;




1.
Transverse wave

-

medium oscillates perpendicular
to direction of wave motion (cannot propagate through a
gas)...examples include wave waves, some spring
waves, and EMR;




http://www.surendranath.org/Applets/Waves/Twave0
1/Twave01Applet.html


http://surendranath.tripod.com/Applets/Waves/Twav
e01/Twave01Applet.html






2.

Longitudinal wave

-

medium oscillates parallel to
direction of wave motion;



http://www.surendranath.org/Applets/Waves/Lwave0
1/Lwave01Applet.html



http://www.mta.ca/faculty/science/physics/suren/
Lwave/Lwave01.html


4.4.4

Wavefront and Ray


Wave Front

-

The continuous line or surface including all the points in space reached by a
wave at the same instant as it travels;

















In this photo of a pond’s surface at the end of a storm, you can see several circular
wave fronts which were created by large drops of water falling off a tree.

Ray

-

The direction of the smallest segment of a wavefront. A ray is drawn as a vector
with the tail at the origin of the wave and the head at the wavefront.

















A ray is drawn from the origin to the wavefront. There are an infinite number of
rays that can be drawn for every wavefront.


4.4.5 and 4.4.6

Wave Terminology: amplitude, period, frequency,
wavelength, periodic wave, medium, wave speed, crest, trough,
compression, rarefaction;



Parts of a Wave

http://id.mind.net/~zona/mstm/physics/waves/partsOfAWave/waveParts.htm



Terminology:


medium

-

material (matter) through which wave energy travels;


displacement

(x)

-

distance medium is moved away from rest position;
measured in meters;


amplitude

(A)

-

maximum displacement of matter away from its equilibrium
position; measured in meters;




period

(
T
)

-

time required for one wave to pass a fixed point; inverse
of frequency; measured in seconds;


frequency

(
f
)

-

number of times medium oscillates completely in 1 s;
inverse of period; measured in waves per second, or, waves s
-
1, or
s
-
1; name of unit: 1.0 s
-
1 = 1.0 Hertz = 1.0 Hz;




f = 1/ T
;
T = 1 / f

;




wavelength

( l)
-

distance between any two successive points (crest
to crest, trough to trough, etc.) on wave; measured in meters;


wave speed

-

rate at which a wave moves through a medium;
measured in ms
-
1;


crest

-

highest point of a transverse wave away from equilibrium
position;


trough

-

lowest point of a transverse wave away from equilibrium
position;


compression

-

place in a longitudinal wave where molecules of
medium are squeezed together (density increased);


rarefaction

-

place in a longitudinal wave where molecules of
medium are pulled apart (density decreased);


• Properties of Sound...an important longitudinal
wave


1. Longitudinal wave with speed = 343 ms
-
1 in air at sea
level at 20.o C;


2. Produced by compression and rarefaction of matter;


3. Sound waves will reflect (echoes), refract, diffract,
constructively and destructively interfere with each other,
produce nodal and antinodal patterns;


4.
Frequency

(f)
range for human hearing is 40. Hz to 20,000. Hz;


5.
Pitch

-

physiological result of a sound wave’s frequency (
f
) on a
living organism; measured on a musical scale with letters
symbolizing certain frequencies (eg., middle C = 262 Hz);


6.
Period

(
T
)
-

time it takes for one full sound wave to pass a point;
measured in seconds; periods for sound audible to humans...

T = 0.025 s ( f= 40. Hz); T = 0.000050 s ( f = 20,000. Hz);


7.
Wavelength

(l) is measured in meters; measured from one
compression to the next compression; wavelengths for sound
audible to humans... l = 8.6 m ( f = 40. Hz); l = 0.017 m ( f = 20,000.
Hz);


8.
Loudness

or
Sound Level

or
Intensity

(wave amplitude)
-

measured from one
compression to the next rarefaction; unit used to
report sound level is the
bel

(named in honor of
Alexander Graham Bell); usually divided into
tenths to give
decibels
; an increase in loudness
of 1 bel or 10 decibels means the sound is 10
times louder!!


9.
Quality

or
Timbre

-

determined by the
combination of harmonics produced by a sound
maker;

4.4.7

Displacement
-
Time and
Displacement
-
Position graphs for
transverse and longitudinal waves;


Displacement / time
-

the motion of one
particle of the medium as the wave energy
moves through the medium


Displacement / position
-

a “picture” of the wave moving through a
medium at one particular instant of time




4.4.8

Derive and apply the relationship between wave speed,
wavelength, and frequency.




speed (v) = distance / time


for a wave: v = l /
T
, measured in ms
-
1;


[wave speed

= wavelength (l) divided by period (
T
)]


since
T
= 1 /
f

,


v

= l
f ,
or


wave speed
= the product of wavelength (l) and frequency (
f
);


------------------------------------------------------------------------------------------------

[*Note: The information found in this set of NOTES is from one or more of
several sources...


1. It is original with this writer;

2. It is taken directly from the IB Curriculum Guide;

3. It is taken from a county textbook: PHYSICS, 2nd Edition, by Kerr, Kerr,
and Ruth, 2001, IBID Press;

4. It is taken from a county textbook: PHYSICS, 5th Edition, by Giancoli,
2002, Prentice Hall;

5. It is taken from a textbook: PHYSICS, 3rd Edition, by Ruth and Kerr,
2007, IBID Press;

6. It is taken from a textbook: STANDARD LEVEL PHYSICS, by Hamper
and Ord, 2007, Pearson Education Limited;

7. It is taken from the myriad of sources called the Internet.


None of the pictures, diagrams, charts and/or graphs are original by this
writer.]