Download Waves

Waves
Wave- A self-propagating disturbance.
Medium- The substance through which the wave propagates.
Source- The object that disturbed the medium to create the wave.
Waves carry or transport energy from the source through the
medium. As the wave passes through one point of the medium,
the medium is disturbed. After the wave has passed, the
medium returns to its original location.
There are three types of waves: Transverse, Longitudinal, and
Surface. For now, we will focus on only longitudinal and
transverse waves. More on surface waves later.
Notice in both this slide and the previous, the waves are moving from
right to left. In a transverse wave, the medium is displaced up and down,
perpendicular to the direction the wave is moving. In the longitudinal
wave, the medium is displaced right and left, parallel to the direction
the wave the wave is moving.
Wavelength- The distance from a point on a wave to the
corresponding point on the next wave. This is a distance, so it is
measured in meters. The symbol for wavelength is λ (lamda) .
All of the red lines shown above are wavelengths of the wave.
The black lines are NOT correct wavelengths.
Amplitude- A measure of the magnitude of the disturbance.
Midline of Vibration (AKA Equilibrium Position)- The “zero
value” of the wave. The value or line about which a wave
oscillates. The point where a wave has zero amplitude.
Crest- The high point of a wave. Point where the wave has
maximum amplitude.
Trough- The low point of a wave. Point where the wave has
minimum amplitude.
Notice in the next picture that the amplitude is measured from
the midline to a crest or from the midline to a trough. Amplitude
is NOT measured from the crest to the trough.
Midline of
Vibration AKA
Equilibrium
Position
Period- The amount of time it takes for a wave to oscillate (vibrate)
once. Measured in seconds. Symbol for period is T.
Frequency- The number of times a wave oscillates (vibrates) in one
second. Measured in Hertz (Hz). 1 Hertz = 1 oscillation per second.
The symbol for frequency is f.
There are two equations that relate Period and Frequency:
T = 1/f
and
f = 1/T
In other words, Frequency and Period
are reciprocals of each other.
As wavelength increases (as the wave gets longer), the frequency
decreases (oscillates fewer times per second)
Notice both of those waves have the same amplitude.
The blue wave has the greatest amplitude, the red wave has the
lowest amplitude.
Notice all the waves have the same wavelength, period, and
frequency.
Sound
Sound is a longitudinal wave. The source of a sound wave is something
vibrating (your vocal cords, some part of a musical instrument,
mosquito’s wings, a stereo speaker etc). The typical medium for sound
is air, but sound can also propagate through liquids (water) and solids
as well.
Sound waves are repeating “zones” of compression and rarefaction
(expansion) caused by the vibrating object vibrating out and squeezing
the air molecules together, then vibrating in and pulling them apart.
Remember, sound travels out in three
dimensions from the source. This is difficult
to show in a two dimensional picture
Notice that the zones of compression are an increase in
atmospheric pressure, and the zones of rarefaction are a
decrease in atmospheric pressure.
At the equilibrium position, the air pressure is normal air
pressure (1.10 x 10^5 Pa), not zero.
As these low and high pressure zones, created by the vibrating object,
hit your ear drum, your ear drum starts to vibrate at the same
frequency. These vibrations are interpreted as “sound” by our brain.
The amplitude of a sound wave is the maximum amount of
difference between normal air pressure and the higher or lower air
pressure in a zone of compression or rarefaction.
The wavelength of a sound wave would be the distance between the
middle of a compression and the middle of the next compression. Or
the distance between the middle of a rarefaction and the middle of
the next rarefaction.
The length of either of the two red lines would be the wavelength of the
sound wave.
For a sound wave:
The amplitude determines the loudness of the sound. Greater
amplitude means a louder sound.
Also, the louder the sound, the more energy a sound wave carries.
The frequency determines the tone or pitch of the sound. Greater
frequency means a higher pitch.
Light is also a wave. However, light does not need a medium to
propagate through. In other words, light can propagate through the
vacuum (emptiness) of space.
Light is only a small part of the electromagnetic spectrum (see picture
on next slide). All the different parts of the electromagnetic spectrum
differ from light only in frequency (and thus period) and wavelength.
Since light does not need a medium to propagate, and ALL other waves
do, we can classify waves as two types:
Mechanical waves- Require a medium to propagate (sound, water
waves, waves on a vibrating string, etc).
Electromagnetic waves- Do not require a medium to propagate (visible
light, radio waves, ultraviolet light, microwaves, etc (see next slide)).
Notice blue light has a shorter wavelength but higher frequency
than red light.
Radio waves have the longest wavelength and lowest frequency.
Electromagnetic (EM for short) waves are an oscillation in the
strength of electric and magnetic fields. Notice these oscillations
are perpendicular to the direction the wave travels, therefore EM
waves are transverse waves.
Notice in the previous picture, the two oscillating fields have the
same wavelength and frequency (and thus same period).
Also notice that the crests and troughs occur at the same
moment.
The source of an EM wave is a vibrating electron. The EM wave
will have the same frequency as the vibrating electron.
For light, the frequency of the wave determines the color. The
amplitude determines the brightness of the light.
For any wave, the speed of the wave can be determined by the
formula
Vwave = frequency of wave times the wavelength of the wave
Vwave = f · λ
(formula # 22)
A wave will always travel at the same speed through a particular
medium. However, if the wave enters a different medium, or if the
medium changes, the speed of the wave will also change.
For example, sound travels faster in cold air than hot air. It also
travels much faster in water than in air.
The waves produced by our wave machines will travel at different
speeds if the thickness, tension, or any other property of the
string were to change.
All the various sounds produced by something like a marching band
travel through the air at the same speed.
All the different instruments will produce sounds of different
wavelengths , frequencies, and amplitudes, but the product of the
wavelength and the frequency (which equals the speed of the sound
wave) will always be the same.
The same is true for light. All the different colors of light travel at the
same speed, even though all the different colors of light have different
frequencies and wavelengths.
In our second wave lab, you varied the frequency of the wave travelling
through the string. This did not change the speed of the wave travelling
along the string, but it did result in a change in the wavelength of the
wave.
Hopefully, you saw this when you multiplied the wavelength by the
corresponding frequency , and got the same value each time.
Waves carry energy from one location or object to
a second location or object.
When a wave hits a surface, three things can happen to the wave
(and the energy it is carrying):
1. Reflection- wave “bounces off” the surface and carries the energy
in a different direction.
2. Absorption- energy is lost by wave (wave disappears) and object or
surface gains the energy the wave was carrying. This gain in energy
can show up as heat, vibration, motion, etc.
3. Transmission- The energy the wave is carrying passes through the
object or substance and creates a new wave on the other side.
Often, more than one of these happens. But energy is ALWAYS
conserved. Any loss of energy by the wave is equal to the gain in
energy by the object.
Reflection– sunlight reflects off the mountain. Some of that reflected light comes
straight to our eyes and we see the mountain.
But some of the reflected light goes toward the water, reflects again off the water,
comes to our eyes, and we see the image of the mountain in the water.
An echo is a reflected sound wave.
Sonar uses reflected sounds waves to detect objects…
…or to map the ocean floors.
Bat sonar (AKA-echolocation) far better than any
man-made sonar:
Whales and Dolphins also use Sonar to detect prey
and other objects.
Two types of Reflection:
1. Diffuse Reflection
and
2. Specular Reflection
Diffuse Reflection- Light rays from an object are
scattered when they are reflected by the uneven surface.
No image of the object is seen on the surface.
Specular Reflection- Light waves coming from an object are
all reflected in the same direction by the smooth surface.
An image of the object can be seen on the surface.
Specular
Reflection
Diffuse
Reflection
Specular
Reflection
Diffuse
Reflection
The bathroom walls produce specular reflection of sound.
This classroom’s walls produce diffuse reflection of sound.
A recording studio’s walls would absorb most sound.
Remember- “white light” from a bulb or the sun is actually
a combination of all colors of the rainbow:
ROYGBIV
The color of an object is determined by the color of light that
is reflected. All the other colors are absorbed.
This is known as selective absorption and reflection.
Or, an object’s color may be due to certain
colors being transmitted instead of absorbed:
The glass that makes up the walls of this fish tank transmits
light. Therefore we can see the fish inside the tank.
Partial Reflection and Partial Transmission
All waves also undergo Refraction and Diffraction
Refraction- The change in direction of a wave as it is
transmitted from one medium to another.
Mirages are due to refraction of light. (see pic next slide).
As light from the sky gets closer to the ground, the hotter air
above the road causes the light to refract before it hits the
road surface. Instead of reflecting off the road in a diffuse
manner (and not producing an image of the sky on the
surface of the road), the light from the sky refracts and gets
to our eyes.
Therefore, we see an image of the sky floating just slightly
above the road, instead of seeing the road.
This image of the sky looks very much like water on the
road.
Note that sound waves can also be refracted when they
pass from hot to cold air, or from humid to dry air, or
vice versa.
The effect of this is that objects can sound like they are
in a different position than they really are, or are closer
or farther away than they really are.
You may have noticed that sound “carries” over calm
water. The cooler, more humid air above the surface of
the water refracts (bends) the sound wave away from
the surface of the water, directing it more toward your
ears, and the object producing the sound (like a distant
boat or a duck) sounds like it is closer to you than it
really is.
Diffraction- The bending of a wave around or behind
an obstacle
Notice the water behind the wave barriers is still
experiencing wave action.
Imagine the “source” to be a person talking in the bathroom. The
“receiver” is one of us in my classroom. We might still hear the person
talking, because the sound wave can diffuse through the bathroom
doorway into the hallway, and then into my classroom.
Normally, radio waves would be blocked by the mountain. But the
house might still be able to tune into the radio station because the
radio waves diffuse behind the mountain to the house.
Waves can be classified as Transverse or Longitudinal,
based on the motion of the wave’s medium in relation to
the direction the wave propagates.
There is a third type of wave called a “surface wave”.
These waves travel along the surface of a medium or along
the boundary between two media. Water waves are
surface waves– they travel along the surface of the ocean
or lake, in between the boundary of the water and the air.
In a surface wave, the medium moves in a circular pattern.
Surface wave:
Notice the size of the circle the medium particles make decreases the
deeper you go.
When you are at the top of the circle, the crest of the wave is directly
over you. When you are at the bottom of the circle, the trough of the
wave is directly over you.
When the water depth is less than half a wavelength, there is friction
between the deeper water and the bottom. This slows the movement of
the bottom of the wave. The top of the wave then moving faster than
the bottom, and the wave begins to “break”.
Earthquakes produce “seismic waves” which are a
combination of longitudinal, transverse, and surface waves.
Black arrow shows the seismic
waves are travelling to the right
S wave: Transverse Wave,
ground moves side to side
P wave: Longitudinal Wave,
ground moves front to back
Surface wave:
Ground moves in a circular motion
P and S waves travel from the location of the earthquake inside the
earth outward in all directions.
P stands for Primary Wave, so named because it travels the fastest
and arrives first. P waves are similar to sound waves due to the
medium being compressed and expanded.
S stands for Secondary Wave, so named because it travels slower
than the P wave, and so arrives second.
Surface waves are generated when the P and S waves reach the
surface. They travel along the surface of the Earth and arrive after
the P and S waves.
Surface waves are the most destructive of the three types of
seismic waves.
Epicenter: Point on the Earth’s surface directly above the location of
an earthquake.
Can be located by a process of Triangulation:
1. Need three locations that detected both the P and S waves
2. Since both waves travel at constant, known speeds, and P waves
are faster, the time between the arrival of the two waves at a
location can be used to determine the distance to the epicenter of
the earthquake. All three locations calculate the distance to the
epicenter.
3. All three locations draw circles on a map. The center of each
circle is the location and the radius of each circle is the distance to
the epicenter.
4. The location where all three circles overlap is the epicenter of the
earthquake
The center of each circle is a location that has detected P and S waves
from an earthquake using a seismograph.
Each location measures the time between the arrival of the P and S
waves, then calculates the distance to the epicenter. The radius of each
circle is that distance.
Where the three circles overlap is the location of the epicenter of the
earthquake.
Damage caused by S- waves
Damage caused by Surface Waves
We know the Earth has a liquid outer core based on the
properties of S and P waves.
S waves can only travel through solids, not liquids.
P waves can travel through both solids and liquids.
When there is an earthquake, both waves travel through the solid
crust and mantle, but only P waves reach the opposite side of the
Earth.
Something blocks the S waves from reaching the other side of the
Earth. That something is the liquid outer core.
S- wave shadow zone
No S waves are detected in the “S wave shadow zone”. However, P
waves are detected everywhere around the globe. The only thing that
would block the S waves is a liquid core at the center of the Earth.