Bike Generator Project
• Each lab section will build 1 bike generator
•Each lab group will
•build 1 energy board
•Connect and test energy board and bike generator
•Create curriculum materials and demos to teach a class
•How current creates a magnetic field
•How a motor works
•How a generator works
•Your hypothesis that students to test while riding bike
•Handouts that explain activities (electronic versions
to me)
•VISIT A CLASS and show demos and do activities
•Each person will produce a formal lab write-up for this
lab project
Transverse and Longitudinal Waves
Transverse and Longitudinal Waves
Wave Speed
The speed of transverse waves on a string stretched with
tension Ts is
where μ is the string’s mass-to-length ratio, also called the
linear density.
EXAMPLE 20.1 The speed of a wave pulse
QUESTION:
EXAMPLE 20.1 The speed of a wave pulse
One-Dimensional Waves
• To understand waves we must deal
with functions of two variables, position and
time.
• A graph that shows the wave’s displacement as
a function of position at a single instant of time
is called a snapshot graph. For a wave on a
string, a snapshot graph is literally a picture of
the wave at this instant.
• A graph that shows the wave’s displacement as
a function of time at a single position in space
is called a history graph. It tells the history of
that particular point in the medium.
EXAMPLE 20.2 Finding a history graph from
a snapshot graph
QUESTION:
EXAMPLE 20.2 Finding a history graph from
a snapshot graph
Sinusoidal Waves
• A wave source that oscillates with simple
harmonic motion (SHM) generates a sinusoidal wave.
• The frequency f of the wave is the frequency of
the oscillating source.
• The period T is related to the wave frequency f by
• The amplitude A of the wave is the maximum value
of the displacement. The crests of the wave
have displacement Dcrest = A and the troughs have
displacement Dtrough = −A.
Sinusoidal Waves
Sinusoidal Waves
• The distance spanned by one cycle of the motion is
called the wavelength λ of the wave. Wavelength is
measured in units of meters.
• During a time interval of exactly one period T, each
crest of a sinusoidal wave travels forward a distance of
exactly one wavelength λ.
• Because speed is distance divided by time, the
wave speed must be
or, in terms of frequency
Sinusoidal Waves
• The angular frequency of a wave is
• The wave number of a wave is
• The general equation for the displacement caused
by a traveling sinusoidal wave is
This wave travels at a speed v = ω/k.
Waves in Two and Three Dimensions
• Suppose you were to take a photograph of
ripples spreading on a pond. If you mark the
location of the crests on the photo, these would be
expanding concentric circles. The lines that locate
the crests are called wave fronts, and they are
spaced precisely one wavelength apart.
• Many waves of interest, such as sound waves
or light waves, move in three dimensions.
For example, loudspeakers and light bulbs
emit spherical waves.
• If you observe a spherical wave very, very far
from its source, the wave appears to be a plane
wave.
Waves in Two and Three Dimensions
Waves in Two and Three Dimensions
Sound Waves
Sound Waves
• For air at room temperature (20°C), the speed of
sound is vsound = 343 m/s.
• Your ears are able to detect sinusoidal sound
waves with frequencies between about 20 Hz and
about 20,000 Hz, or 20 kHz.
• Low frequencies are perceived as “low pitch”
bass notes, while high frequencies are heard as “high
pitch” treble notes.
• Sound waves exist at frequencies well above 20
kHz, even though humans can’t hear them. These are
called ultrasonic frequencies.
• Oscillators vibrating at frequencies of many
MHz generate the ultrasonic waves used in
ultrasound medical imaging.
Test your hearing
• www.phys.unsw.edu.au/jw/hearing.html
EXAMPLE 20.6 Sound wavelengths
QUESTION:
EXAMPLE 20.6 Sound wavelengths
Electromagnetic Waves
• A light wave is an electromagnetic wave, an
oscillation of the electromagnetic field.
• Other electromagnetic waves, such as radio
waves, microwaves, and ultraviolet light, have the
same physical characteristics as light waves even though
we cannot sense them with our eyes.
• All electromagnetic waves travel through vacuum
with the same speed, called the speed of light. The value
of the speed of light is c = 299,792,458 m/s.
• At this speed, light could circle the earth 7.5 times in
a mere second—if there were a way to make it go
in circles!
The Index of Refraction
• Light waves travel with speed c in a vacuum, but
they slow down as they pass through transparent
materials such as water or glass or even, to a very
slight extent, air.
• The speed of light in a material is characterized by
the material’s index of refraction n, defined as
Power and Intensity
EXAMPLE 20.9 The intensity of a laser beam
QUESTION:
EXAMPLE 20.9 The intensity of a laser beam
EXAMPLE 20.9 The intensity of a laser beam
Intensity and Decibels
• Human hearing spans an extremely wide range
of intensities, from the threshold of hearing at ≈ 1 ×
10−12 W/m2 (at midrange frequencies) to the threshold
of pain at ≈ 10 W/m2.
• If we want to make a scale of loudness, it’s
convenient and logical to place the zero of our scale at
the threshold of hearing.
• To do so, we define the sound intensity level,
expressed in decibels (dB), as
where I0 = 1 × 10−12 W/m2.
Intensity and Decibels
The Doppler Effect
• An interesting effect occurs when you are
in motion relative to a wave source. It is called
the Doppler effect.
• You’ve likely noticed that the pitch of
an ambulance’s siren drops as it goes past you.
A higher pitch suddenly becomes a lower pitch.
• As a wave source approaches you, you will
observe a frequency f+ which is slightly higher than
f0, the natural frequency of the source.
• As a wave source recedes away from you, you
will observe a frequency f− which is slightly lower
than f0, the natural frequency of the source.
The Doppler Effect
The frequencies heard by a stationary observer when
the sound source is moving at speed v0 are
The frequencies heard by an observer moving at speed
v0 relative to a stationary sound source emitting
frequency f0 are
EXAMPLE 20.11 How fast are the police
traveling?
QUESTION:
EXAMPLE 20.11 How fast are the police
traveling?
Snapshot and History Wave Activity
• PHET and Matlab
• phet.colorado.edu/sims/wave-on-a-string/wave-on-astring_en.html
• Turn on the ruler and create a snapshot graph (amplitude vs.
displacement graph)
• Select a green bead and center the left side of the ruler on it
• Turn on the timer
• Choose oscillate and pause the simulation to collect amplitude
and time data for that green bead
• Record your data in Matlab
• Plot and fit your data to create a history graph (amplitude vs.
time)