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Principle of Superposition of Waves · Principle of Superposition of Waves Two important concepts...

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Page 1: Principle of Superposition of Waves · Principle of Superposition of Waves Two important concepts that physicists study are _Wave Motion _article Motion This lecture will begin with
Page 2: Principle of Superposition of Waves · Principle of Superposition of Waves Two important concepts that physicists study are _Wave Motion _article Motion This lecture will begin with

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.

Page 3: Principle of Superposition of Waves · Principle of Superposition of Waves Two important concepts that physicists study are _Wave Motion _article Motion This lecture will begin with

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.

Page 4: Principle of Superposition of Waves · Principle of Superposition of Waves Two important concepts that physicists study are _Wave Motion _article Motion This lecture will begin with

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.

Page 5: Principle of Superposition of Waves · Principle of Superposition of Waves Two important concepts that physicists study are _Wave Motion _article Motion This lecture will begin with

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.

Page 6: Principle of Superposition of Waves · Principle of Superposition of Waves Two important concepts that physicists study are _Wave Motion _article Motion This lecture will begin with

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.

Page 7: Principle of Superposition of Waves · Principle of Superposition of Waves Two important concepts that physicists study are _Wave Motion _article Motion This lecture will begin with

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.

Page 8: Principle of Superposition of Waves · Principle of Superposition of Waves Two important concepts that physicists study are _Wave Motion _article Motion This lecture will begin with

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.

Page 9: Principle of Superposition of Waves · Principle of Superposition of Waves Two important concepts that physicists study are _Wave Motion _article Motion This lecture will begin with

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.

Page 10: Principle of Superposition of Waves · Principle of Superposition of Waves Two important concepts that physicists study are _Wave Motion _article Motion This lecture will begin with

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.

Page 11: Principle of Superposition of Waves · Principle of Superposition of Waves Two important concepts that physicists study are _Wave Motion _article Motion This lecture will begin with

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.

Page 12: Principle of Superposition of Waves · Principle of Superposition of Waves Two important concepts that physicists study are _Wave Motion _article Motion This lecture will begin with

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

Page 13: Principle of Superposition of Waves · Principle of Superposition of Waves Two important concepts that physicists study are _Wave Motion _article Motion This lecture will begin with

720 m/s and a wavelength of 16 m, follow the

calculations below.

Page 14: Principle of Superposition of Waves · Principle of Superposition of Waves Two important concepts that physicists study are _Wave Motion _article Motion This lecture will begin with

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