Waves. Definitions of Waves A wave is a traveling that carries through space and matter without...
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Transcript of Waves. Definitions of Waves A wave is a traveling that carries through space and matter without...
Waves
Definitions of Waves A wave is a traveling that
carries through space and matter without transferring . Transverse Wave: A wave in which the
disturbance occurs to the direction of travel.
• A type of transverse wave is Longitudinal Wave: A wave in which the
disturbance occurs to the direction of travel of the wave.
• A type of longitudinal wave is Surface Wave: A wave that has charact-
eristics of both and waves.
Types of Waves
Mechanical Waves: Require a such as
, , of a spring or the fabric of a rope. Electromagnetic Waves:
can travel in the absence of a medium.
Transverse Wave Characteristics Crest: . Trough: . Amplitude:
(undisturbed position).
John Wiley & Sons
Transverse Wave Characteristics (cont.)
Frequency(f): The number of the wave makes in
The unit for frequency is
Wavelength(): The minimum at which the wave repeats the
same pattern A single oscillation is also called a The units for wavelength are
Transverse Wave Characteristics (cont.)
Velocity (v): of the wave Measured in
The formula to calculate the speed of a wave is
Period (T): it takes for the wave to complete one The units for period is The formula to calculate the period is
Transverse vs. Longitudinal Waves
The Relationships v = f
The of a wave is determined by the in which it travels.
That means that for a given medium
• and are inversely proportional.
• As one , the other
Wavelength
Frequency
The Inverse RelationshipsT =
As the period , the .
Period
Frequency
Speed of a Wave on a String For a stretched rope or string:
Where: = Tension = linear density =
As the tension , the speed . As the mass , the speed . This phenomena is commonly seen in
v =
Waves at Boundaries A wave incident upon a
fixed boundary will have its reflected back in the opposite direction. Note that the wave pulse is
after reflecting off the boundary.
www.electron4.phys.utk.edu
Interference
occurs whenever two waves occupy the same space at the same time. Law of :
When two or more waves are present at the same time at the same place, the
disturbance is equal to the of the disturbances from the individual waves.
Wave Interference
www.electron4.phys.utk.edu
Interference – Process by which two waves meet producing a net
amplitude.
Wave Interference
Interference – Process by which two waves meet
out each other.
Waves
Wave: An interference pattern resulting from two waves moving in directions with the same and
such that they develop a consistent repeating pattern of
and interference.
Waves
Node: The part of a standing wave where interference is at all times ( o out of phase).
Antinode: The part of the wave where interference is maximized
( ).
Waves When a wave impacts a boundary, some
of the energy is , while some passes , or may be
. The wave that passes through is called a
wave. A wave that is transmitted through a
boundary will lose some of its energy. Electromagnetic radiation will both
down and have a wavelength when going into a denser
media. Sound will when
transitioning into a denser media.
Incident + Reflected Wave
Higher speed
Longer wavelength
Lower speed
Shorter wavelength
Transmitted Wave
Continuous Waves – Higher Speed to Lower Speed Note the differences in wavelength and amplitude between
of the wave in the two different mediums
Displacement
Boundary
v1 v2-v1
Note: This phenomena is seen with light traveling from air to water.
The Wave Equation waves can be
represented by the following equation.
y(x,t) = ymsin(t - x) Where:
ym = = (2/)x = = (2f)t =
Note that the sum (t - x) is in , not degrees.
+x
The Wave Equation
y(x,t) = ymsin(t - x)
= 2/
Waveformrepeats itself every .
= 2f
Waveformtravels through 1
(T) every . A phase constant () can be included in the phase that represents
all waves that do not pass through the origin.
The Wave Equation – An Alternate Representation
y(x,t) = ymsin(t - x)
Substituting for (2f), (2/) and ym (A) yields:
y(x,t) = Asin2(ft - x)or
y(x,t) = Asin2(vt - x)
1
Key Ideas Waves transfer without transferring
. Longitudinal waves like that of sound require a
. Transverse waves such as electro-magnetic
radiation (light) do not require a . In transverse waves, displacement is
to the direction of the wave while in longitudinal waves, the displacement is
.
Key Ideas Waves can with one
another resulting in or interference.
waves are a special case of constructive and destructive interference for two waves moving in opposite directions with the same
, and .