
Physics of Technology PHYS 1800. Lecture 35 Waves. PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet. *Homework Handout. Physics of Technology PHYS 1800. Lecture 35 Waves. Examples of Wave Phenomena. Wave motion describes phenomena ranging from the familiar... Ocean waves.
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PHYSICS OF TECHNOLOGYSpring 2009 Assignment Sheet
*Homework Handout
Wave motion describes phenomena ranging from the familiar...
Ocean waves...
waves...
(gravity waves).
Energy added by doing work to stretch the spring is transformed back and forth between potential energy and kinetic energy.
Oscillatory Motion
X(t) = A sin (2π f t)
Why does a swinging pendant return to the same point after each swing?
The force does work to move the ball. This increases the ball’s energy, affecting its motion.
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Compressionand Oscillation on an Atomic ScaleBonds between atoms in a compressed solid can be treated as compressed springs.
Ultimately the forces come from electrostatic interactions between electrons and protons (and a little quantum mechanics).
Fspring=-k Δx
What Are Waves?
What is actually moving?
Do the waves carry energy?
A Slinky is ideal for studying simple waves.
longitudinal.
electromagnetic waves
are transverse.
associated with
transverse waves but
not longitudinal waves.
both longitudinal and
transverse properties.
Longitudinal Waves
Longitudinal Waves
Wavelength
a) 1/6 m b) 1 m c) 2 m d) 3 m e) 6 m
In 6 m, the wave goes through 2 complete cycles.
The wavelength (length of one complete cycle) is (6 m)/2 = 3 m.
Frequency of a Wave
a) 1/6 m/s b) 2/3 m/s c) 2 m/s d) 3 m/s e) 6 m/s
causes this next segment
to accelerate upward, and
so on down the rope.
depends on how fast
succeeding segments can be
started moving (accelerated).
A rope has an overall length of 10 m and a total mass of 2 kg. The rope is stretched with a tension of 50 N. One end of the rope is fixed, and the other is moved up and down with a frequency of 4 Hz. What is the speed of waves on this rope?
Velocity of a Wave
a) 5.0 m/s b) 7.07 m/s c) 15.8 m/s d) 50 m/s e) 250 m/s
A rope has an overall length of 10 m and a total mass of 2 kg. The rope is stretched with a tension of 50 N. One end of the rope is fixed, and the other is moved up and down with a frequency of 4 Hz. What is the wavelength?
Wavelength of a Wave
a) 0.20 m b) 3.95 m c) 10 m d) 15.8 m e) 25 m/s
the two identical segments
will combine to form a larger
wave on the single joined
rope.
individual waves will add
together to form a wave with
the same frequency and
wavelength but twice the
height of the initial two waves.
When two or more waves combine, the resulting disturbance or displacement is equal to the sum of the individual disturbances.
upward when the other
wave is moving downward,
the two waves are
completely out of phase.
same height, the resulting
combined displacement will
be zero.
not moving at all.
the nodes and
antinodes, the
amplitude has
intermediate
values.
producing a higher-pitched
tone.
may also be produced.
producing a higher-pitched
tone.
may also be produced.
A guitar string has a mass of 4 g, a length of 74 cm, and a tension of 400 N. These values produce a wave speed of 274 m/s. What is its fundamental frequency?
A guitar string has a mass of 4 g, a length of 74 cm, and a tension of 400 N. These values produce a wave speed of 274 m/s. What is the frequency of the second harmonic?
The bass string has been plucked, producing a blur near the middle where the amplitude is greatest.
waves travel with a speed of
340 m/s or 750 MPH.
speed also depends on the
masses of the molecules or
atoms.
through liquids and solids, often
with higher speeds.
wave can be found from the
speed of sound in air and the
wavelength:
where the wavelength is
determined by the length of
the tube.
also determines which
harmonics will be
reinforced.
tones.
lot of higher harmonics
so it sounds “bright”
or “brassy”.
tone dominated by the
fundamental frequency,
with almost none of the
higher harmonics, so
the tone sounds “pure”.
a fifth, between the first
and fifth notes in the scale
(C and G).
harmonic is 4/3 that of the
third harmonic. This
interval is a fourth,
between the first and
fourth notes (C and F).
adjacent half steps on
the scale are all identical,
so the scales sound
correct regardless of
what key you are in.
A C-major scale begins with do on middle C having a frequency of approximately 264 Hz. Assuming that they have been tuned to the perfect ratios for the intervals in question, what should the frequency be for sol (G)?
A C-major scale begins with do on middle C having a frequency of approximately 264 Hz. Assuming that they have been tuned to the perfect ratios for the intervals in question, what should the frequency be for fa (F)?
A C-major scale begins with do on middle C having a frequency of approximately 264 Hz. Assuming that they have been tuned to the perfect ratios for the intervals in question, what should the frequency be for do at the top of the scale (high C)?
Alternating Current and Household Circuits
increasing the fastest,
the voltage is a
maximum; when the
flux is decreasing the
fastest, the voltage is
a maximum in the
other direction
(negative).
James Clerk Maxwell
c is speed of EM waves (light)
Hetrz (1888) showed EM waves:
have speed c
have wavelength
have both E and M components
reflect
Refract
Interfere
diffract
Electromagnetic WavesThese are all forms ofelectromagnetic waves.Although seemingly quite different, they share many properties, including a, b, and c.
Fizeau’s wheel for measuring the speed of light
Electromagnetic Spectrum
= 10 m f = v /
v = c = 3 x 108 m/s = (3 x 108 m/s) / 10 m
v = f = 3 x 107 Hz
color
different colors
BLUE
Next Lab/Demo: Electric Circuits
Magnetism
Thursday 1:30-2:45
ESLC 46
Ch 13 and 14
Next Class: Friday 10:30-11:20
BUS 318 room
Read Ch 14