Principle of Superposition of Waves · Principle of Superposition of Waves Two important concepts...
Transcript of Principle of Superposition of Waves · Principle of Superposition of Waves Two important concepts...
Principle of Superposition of Waves
Two important concepts that physicists study are
Wave Motion _
_article Motion
This lecture will begin with the study of wave
motion. Particle motion will be studied later in the
next semester.
The first thing will show what happens when two
waves are occupying the same region of a medium
(the material or substance that propagates a
disturbance or wave)
at the same time.When this happens the waves
interfere with each other and the combined waves
take on a new shape.
You will learn how to determine that shape.
First let’s review the basic parameters of a
transverse wave.
Next let’s look at the superposition of some simple
combinations of two waves .The first addition of waves
that will be described involves two waves that are in
phase ( A crest of one wave is positioned with the
crest of the other wave. The same can be said for
troughs) This is referred to as Constructive
interference.
This represents the displacement by the white wave
alone. This represents the displacement by the orange
wave alone. Since they are both displacements on the
same side of the baseline, they add together. Just
repeat this step for several points along the waves.
The next addition of waves that will be described
involves two waves that are out of phase.( A crest of
one wave is positioned with a trough of the other wave)
This is referred to as destructive interference.
This represents the displacement by the white wave
alone.
This represents the displacement by the orange wave
alone.Since the two displacements are on opposite
sides of the baseline,
The top one should be considered positive and the
bottom one negative.
Just add the positive and negatives together like this.
Repeat this step for several points along the waves.
Finally we observe two waves that are partially in
phase. A different method of adding the waves will be
demonstrated.
From the baseline measure to the “white” wave. Then
add this to the “orange” wave.
By overlaying the constructive interference curve from
a previous one you can tell that the curve of this slide
is not fully constructive interference.
Interference Animation
The frequency of a wave is the number of waves
passing a stationary point per second. It is
sometimes expressed as so many waves per second,
so many cycles per second, or so many oscillations
per second.
The period of a wave is the time required for one
vibration. It is also the time for a wave to travel
one wavelength.
Period (T) and frequency (f) are inversely related.
In symbolic form
For a wave, if the distance traveled is a wavelength
(), then the time to travel this distance is the period
(T ).
Since the average speed is defined as a distance
divided by the time.
Thus if the experimenter can measure two of the
three quantities v, l, and f, then the third can be
calculated.
Please note that speed and velocity are two different
descriptors of motion. You will learn more details
about these descriptors in the second half of this
course. What is important for you to understand at
this point is that the symbol v being used in formulas
throughout the manual and the lecture shows
represents speed, not velocity, although most of the
time it also will represent the magnitude of the
velocity.
The difference between speed and velocity
Just as distance and displacement have distinctly
different meanings (despite their similarities), so do
speed and velocity. Speed is a scalar quantity that
refers to "how fast an object is moving." Speed can be
thought of as the rate at which an object covers
distance.
A fast-moving object has a high speed and covers a
relatively large distance in a short amount of time.
Contrast this to a slow-moving object that has a low
speed; it covers a relatively small amount of distance in
the same amount of time. An object with no movement
at all has a zero speed.
Velocity is a vector quantity that refers to "the rate
at which an object changes its position." Imagine a
person moving rapidly - one step forward and one step
back - always returning to the original starting position.
While this might result in a frenzy of activity, it would
result in a zero velocity.
Because the person always returns to the original
position, the motion would never result in a change in
position. Since velocity is defined as the rate at which
the position changes, this motion results in zero
velocity. If a person in motion wishes to maximize their
velocity, then that person must make every effort to
maximize the amount that they are displaced from
their original position.
For certain, the person should never change directions
and begin to return to the starting position.
Velocity is a vector quantity. As such, velocity
is direction aware. When evaluating the velocity of an
object, one must keep track of direction. It would not
be enough to say that an object has a velocity of 55
mi/hr. One must include direction information in order
to fully describe the velocity of the object. For
instance, you must describe an object's velocity as
being 55 mi/hr, east. This is one of the essential
differences between speed and velocity. Speed is a
scalar quantity and does not keep track of direction;
velocity is a vector quantity and is direction aware.
How to manipulate the Hertz (Hz) unit.
Just remember that one Hz is the same as
1/second (1/s).
Example: What is the speed of a wave of frequency
500 Hz and wavelength of 2 meters?
The example below illustrates that units in equations
can be manipulated just like numbers in equations. To
determine the frequency of a wave that has a speed of
720 m/s and a wavelength of 16 m, follow the
calculations below.