Chapter 15 Types and Applications of Waves
I.
Guitars and Waves
A.
Apply what we know about waves to guitar strings
1) Medium = wire, with known tension (F), m, velocity
2) Generate a transverse standing wave by plucking the wire
a) Wave in the wire causes a sound wave in the air nearby
b) Frequency (f) of sound wave = f of the standing wave in string
c) Higher f gives a higher pitch, lower f gives a lower pitch
B.
Guitar string standing waves
1) Only certain standing waves are possible for each
string with given L
a) Standing wave must have nodes at ends
because that is where the strings attach
b) Standing waves can have large or small
amplitude (loud or soft)
c) Vibrations of string creates sound waves
2)
3)
Longest possible wavelength (shortest frequency, v = fl) is called the
v
v
Fundamental or First Harmonic (f1)
f1  
l 2L
a) l = 2L for the longest possible standing wave
b) Length (L) changes the frequency and the pitch we hear (fretting)
c) Change in velocity (F, m) also change f and the pitch we hear
i. Tune the guitar by adjusting the tension of the string (F)
ii. Heavy strings give lowest sounds (wire wrapped for mass) (m)
Next longest possible standing wave has l = L
a) Frequency is twice as large as fundamental
b) Higher pitch, actually 1 octave higher
c) Called Second Harmonic
v
v
f 2    2 f1
l L
v
f1 
v
l

v
3v
f3  

 3f1
l 2/3L 2L
4)
Third Harmonic has l = 2/3 L
a) Frequency is three times that of the fundamental
b) Higher pitch, a fifth above f2
5)
Guitar string problem: with m = 4 g, L = 75 cm, F = 400 N, v = 274 m/s
v 274m / s

 183 / s  183Hz
2L
1.5m
You try finding f2
II.
Sound Waves
A.
What are sound waves?
1) Vibrating guitar string can make sound waves, but so can a car crash, a
stereo, or a crying baby
2) Since we can hear them, they must travel through air (medium) to ears
3) Generation of Sound Waves by a stereo
a) Oscillating electric current causes
a magnet to oscillate
b) Magnet causes an attached diaphram
at the same frequency
c) Diaphram compresses nearby air in
a regular pattern with same f
d)
Sound wave = periodic longitudinal wave of air compressions that
propagates out in every direction (to our ears)
e)
f)
g)
We can hear f = 16 Hz—20,000 Hz of air compressions (pitch)
Loudness depends on amplitude (how much air is compressed)
Graph of pressure vs. distance shows sin wave nature of sound
B.
Speed of Sound
1) In room temp. air, sound travels at v = 340 m/s = 750 mph (1 mile in 5 s)
2) Light travels much faster
3) See contact of a batted ball before you hear it
4) See lightning before hear thunder
a) Tell how far away lightning is by counting until you hear thunder
b) 5 s = 1 mile, 10 s = 2 mile, 15 s = 3 mile etc…
5)
What determines speed of sound?
a) Velocity depends on properties of the medium (air)
b) How fast air molecules transmit energy to each other depends on
how often they collide. KE + PE = U = temperature
c) DT of 10 oC gives Dv of 6 m/s for air
6)
Can sound travel through liquids or solids?
a) Molecules are much closer
b) Transmit pressure changes much faster
c) Speed of sound in water = 4 x speed of sound in air
d) Speed of sound in steel = 4 x speed of sound in water = 16 x air
C.
Wind Instruments
1) Standing waves in guitar string give sounds of certain pitch
2) Standing sound waves in a pipe give us similar pitch control
a) Incoming and reflected sound waves interfere to give standing wave
b) Node at bottom, Antinode at opening so we can hear it
3) Fundamental has largest possible wavelength
a) Node—Antinode distance = l/4
b) l = 4L for the fundamental of a pipe
c) Find f of the fundamental of v = 340 m/s, L = 0.25 m (Pop Bottle)
f1 
4)
5)
6)
v
l

v 340m / s

 340 Hz
4L
1.0m
“Middle C” has f = 264 Hz, so our pop
bottle pitch is higher than middle C
Second Harmonic has l = 4/3 L, find that
f = 1020 Hz (higher than f1)
Third Harmonic has l = 4/5L,
f = 1700 Hz
D.
Doppler Effect
1) The sound made by an approaching object seems higher pitched than it is
2) The sound made by an retreating object seems lower pitched than it is
3)
Motion of the source changes the wavelength on both sides of the source
III. Electromagnetic Waves
A.
What are Electromagnetic Waves
1) Form of energy having an electric field and a magnetic field component
2) Gravity can be thought of as a field surrounding any object with mass
3) Electric Field = property of space near a (+) or (-) charged object (E)
4) Magnetic Field = property of space near moving charged objects (B)
5)
B.
Electromagnetic Wave = transverse wave made up of propagating
electric and magnetic fields
Velocity of Electromagnetic Waves
1) Fizeau Designed an experiment to find the velocity of light (an EM wave)
2)
3)
Know: how fast toothed wheel is spinning, distance traveled
Calculate velocity of light = c = 3 x 108 m/s
4)
5)
C.
c is constant for all forms of EM waves traveling in a vacuum
c changes very little for other media
Kinds of Electromagnetic Waves
1) Light, Infrared, Microwaves, etc… are all part of the EM Spectrum
2) v = fl
c = fl = 3 x 108 m/s
3) Each type of EM wave has a range of l and f
Find f for radio wave of l = 10 m and for light wave of l = 6 x 10-7 m
4)
3x108 m / s
c  fl  f  
 3x107 Hz
l
10m
c
f
c
l

3x108 m / s
7
6 x10 m
 5 x1014 Hz