2

Waves are everywhere in nature

– Sound waves,

– visible light waves,

– radio waves,

– microwaves,

– water waves,

– sine waves,

– telephone cord waves,

– stadium waves,

– earthquake waves,

– waves on a string,

– slinky waves

3

What is a wave?

• a wave is a disturbance that travels

through a medium from one location to

another.

• a wave is the motion of a disturbance

• waves transfer energy without the bulk

transport of matter

4

Frequency and Period

• Frequency measures the number of events

that occur in a certain amount of time.

• Period is the time to complete one cycle.

• For example, if you get a paycheck twice a month, the

frequency of payment is two per month (2 paychecks/month)

and the period between checks is half a month.

Frequency (f)- the number of complete cycles per unit time

measured in units of Hz (s-1)

Period (T) - the shortest time interval duringwhich the motion repeats itself

measured in units of time (s, min)

T = 1/f & f = 1/T

Eg. A pendulum bob takes 3.5 s to swing “to and fro”

Eg. Five crests pass a point every second so

f = 5 cycles/s = 5 Hzhttp://www.absorblearning.com/physics/demo/units/DJFPh064.html#Waveperiodandfrequency

f = cyclestime

T = timecycle

Sample Problems1. A child on a swing completes 20 cycles in 25 s. Calculate the

frequency and the period of the swing.

2. A stroboscope is flashing so that the time interval between

flashes is 1/80 s. Calculate the frequency of the strobe light’s

flashes.3. Calculate the frequency and the period of a tuning fork that

vibrates 24 000 times in 1.00 min.

Page 10 #2, page 17 #8 – 13 (don’t convert to s for 9 &10)

Recall:

a wave is a disturbance

that travels through a

medium from one

location to another.A single disturbance is

called a pulse or shock wave

The slinky as a whole does not move

forward, but its different parts move up

and down about their mean positions. It

is only the hump or the disturbance,

which moves forward along the slinky.

The displacement of the particlesof the medium is perpendicular to

the direction of wave propagation (pulse).

TRANSVERSE

e.g. skipping ropes, radio waves, light waves, heat waves, stadium wave

Transverse Waves

The stadium "wave" travels all around the stadium. None of the fans

travel around the stadium. They only stand up and sit down.

That means the movement of the medium (the people) transects (is

perpendicular to) the movement of the wave making this a Transverse

Wave!

LONGITUDINALThe displacement of the particles of the

medium is parallel to the direction of wave propagation (pulse).

e.g. sound waves, tsunami waves, earthquake P waves

Longitudinal Waves

The particles do not move down the tube with

the wave; they simply oscillate back and forth

about their individual equilibrium positions.

SURFACE

A combination of transverse and longitudinal.

The particles move perpendicular and parallel to the pulse.

e.g. water waves, Rayleigh earthquake waves

20

Anatomy of a Wave

• The points A and F are called the CRESTSof the wave.

• This is the point where the wave exhibits the maximum amount of positive or upwards displacement

crest

21

Anatomy of a Wave

• The points D and I are called the TROUGHS of the wave.

• These are the points where the wave exhibits its maximum negative or downward displacement.

trough

22

Anatomy of a Wave cont.

• The distance between the dashed line and

point A (or point D, F or I) is called the

Amplitude of the wave.

• This is the maximum displacement that the

wave moves away from its equilibrium.

Amplitude

23

Anatomy of a Wave cont.

• The distance between two consecutive similar points (in this case two crests) is called the wavelength (λ).

• This is the length of the wave pulse.

• Between what other points can a wavelength be measured?

wavelength

• Recall: The distance between two

consecutive similar points is called the

wavelength (λ). Wavelength can also be

calculated for a longitudinal wave.

Parts of a Longitudinal Wave

Phase

Points along a transverse or longitudinal wave are said to be in phase if they are moving in the same direction and

have the same amplitude.

Which other points are in phase with A?

E, I. They are moving in the same direction AND have the same amplitude.

Are C and G in phase with A?

They are moving out of phase with A because they have the same amplitude but are moving in the OPPOSITE direction.

Sample Problems:

1. Give two examples of each of the three types of energy transfer.

2. What is the difference between a wave and a pulse?

3. Sharon is lying on a raft in a wave pool. Describe to Sharon, in

terms of the waves she is riding, each of the following: amplitude,

period, wavelength, speed, frequency.

4. For the wave pictured,

a. state the value of the λ;

b. state the value of the amplitude;

c. state the number of positive pulses;

d. name the type of wave;

e. label two pulses that are in phase;

f. label two pulses that are out of phase.

5. If you want to increase the amplitude of a pulse, what must you

do to the amount of energy used to make the pulse?

Practice Problems

- Discuss questions

- Lab: Wave Properties

• Assignment: Wave Characteristics

Wave Speed

• We can use what we know to

determine how fast a wave is moving.

What is the formula for velocity?

velocity = distance / time

What distance do we know about a wave?

wavelength

And what time do we know?

period

37

Wave Speed• v = / T and T = 1 / f

• so we can also write

v = f

– velocity = frequency * wavelength

• This is known as the wave equation.

Sample Problems:1) A wave coming in from the ocean has a wavelength of

0.080m. If the frequency of the wave is 2.5 Hz, what is

its speed?

Sample Problems:2) The distance between successive crests of water waves is

4.0m and the crests travel 9.0 m in 4.5 s. What is the

frequency of the waves? What is the period?

42

Wave Behavior

• We know that waves travel through

mediums.

• But what happens when that medium runs

out?

43

Boundary Behavior

• The behavior of a wave when it reaches the

end of its medium is called the wave’s

BOUNDARY BEHAVIOR.

• When one medium ends and another begins,

that is called a boundary.

44

Fixed End

Reflection

• One type of boundary that a wave may encounter is that it may be attached to a fixed end.

• Fixed-end reflection occurs when a wave strikes a rigid barrier.

• In this case, the end of the medium will not be able to move.

• What is going to happen if a wave pulse goes down this string and encounters the fixed end?

45

Fixed End Animation

46

Fixed End

Reflection

• Here the incident pulse is an upward pulse.

• The reflected pulse is upside-down. It is

inverted.

– A crest is reflected as a trough and vice versa.

• The reflected pulse has the same speed, wavelength,

and amplitude as the incident pulse.

• A portion of the energy carried by the pulse is transmitted

to the pole, causing the pole to vibrate.

47

Free End

Reflection

• Another boundary type is when a wave’s

medium is attached to a stationary object as

a free end.

• In this situation, the end of the medium is

allowed to slide up and down.

• What would happen in this case?

48

Free End Animation

49

Free End

Reflection

• If the reflection occurs at a free-end the

reflected pulse is not inverted (erect).

• It is identical to the incident pulse, except it

is moving in the opposite direction.

• The speed, wavelength, and amplitude are

the same as the incident pulse.

50

Change in Medium

• Our third boundary condition is when the medium of a wave changes.

• Think of a thin rope attached to a thick rope. The point where the two ropes are attached is the boundary.

• At this point, a wave pulse will transfer from one medium to another.

• What will happen here?

Less Dense to More Dense

Medium

52

Change in

Medium

• 1. Fast (thin) medium into a slow (thick) medium.

– The slow medium acts as a barrier.

– The transmitted pulse travels slower than the reflected

pulse, is upright and has a shorter wavelength than the

incident pulse.

– The reflected pulse is inverted.

– The speed & λ of the reflected pulse are the same as the

speed and λ of the incident pulse; amplitude decreases

53

Change in Medium

• Think of a thick rope attached to a thin rope. The point where the two ropes are attached is the boundary.

• At this point, a wave pulse will transfer from one medium to another.

• What will happen here?

54

Change in Medium Animation

55

Change in

Medium

• 2. Slow (thick) medium into a fast (thin) medium

– The fast medium does not act as a barrier.

– The transmitted pulse is faster, is upright (erect) and has

a longer wavelength than the incident pulse.

– The reflected pulse is not inverted (it is erect).

– The speed & λ of the reflected pulse are the same as the

speed and λ of the incident pulse; amplitude decreases

Check Your Understanding

http://www.physicsclassroom.com/class/waves/u10l3a.cfm

Check Your Understanding

Sample Problems1) A negative pulse is sent along a spring. The spring is attached to a

light thread that is tied to the wall.

a) Describe the speed and type of pulse that is transmitted at A.

b) Describe the speed and type of pulse that is reflected at A.

c) Describe the speed and type of pulse that is reflected at B.

Sample Problems2) A long spring runs across the floor of a room and out the door. A

pulse is sent along the spring. After a few seconds, an inverted pulse

returns. Is the spring attached to the wall in the room or is it lying

loose on the floor?

Sample Problems1) You want to increase the wavelength of waves in a rope.

Should you shake the rope with a high frequency or a low frequency?

Should you send a pulse from a thin material into a thick material or

send the pulse the other direction?

Practice Problems

Laws of Reflection

• The shape of a continuous crest or trough is

called a wavefront.

• If a wavefront hits a straight barrier, the

wavefront is reflected back along the

original path.

• If the wavefront hits a straight barrier at an

angle (angle of incidence), the wavefront is

reflected at an angle (angle of reflection).

• The angles are measured from the normal,

a line that is perpendicular to the barrier.

Video: Physics Demos in Sound & Waves

Part I

28 min – 29:30 min

• If the wave front approaches a parabolic

barrier, the waves are reflected to a point

called the focal point.

• The normal of a parabolic reflector is

perpendicular to the tangent (normal) at that

point.

Video: Physics Demos in Sound & Waves

Part I

• 29:50 min – 30:05 min

Sample Problems1. The diagram shows wave fronts striking a barrier.

a) Draw the incident direction.

b) Draw the normal.

c) Measure the angle of incidence.

d) Draw the reflected direction.

e) Draw the reflected wave fronts.

2. The diagram shows the direction of a wave that strikes a curved barrier.

a) Draw the tangent line.

b) Draw the normal.

c) Measure the angle of incidence.

d) Draw the reflected direction.

e) Draw the reflected wave fronts.

• HO: Drawing & Measuring Waves

70

Wave Interaction

• All we have left to discover is how waves

interact with each other.

• When two waves meet while traveling

along the same medium it is called

INTERFERENCE.

71

Constructive Interference

• Let’s consider two waves moving towards

each other, both having a positive upward

amplitude.

• What will happen when they meet?

Interference

the result of the superpositionof two or more waves

Principle of Superposition

the displacement of the medium whentwo or more waves pass through

it at the same time is the algebraicsum of the displacements caused

by the individual waves

73

Constructive Interference

• Let’s consider two waves moving towards

each other, both having a positive upward

amplitude.

• What will happen when they meet?

74

Constructive Interference• They will ADD together to produce a

greater amplitude.

• This is known as CONSTRUCTIVE

INTERFERENCE.

• http://zonalandeducation.com/mstm/physics

/waves/interference/constructiveInterferenc

e/InterferenceExplanation2.html

Constructive Interference

78

Destructive Interference

• Now let’s consider the opposite, two waves

moving towards each other, one having a

positive (upward) and one a negative

(downward) amplitude.

• What will happen when they meet?

79

Destructive Interference

• This time when they add together they

will produce a smaller amplitude.

• This is know as DESTRUCTIVE

INTERFERENCE.

http://zonalandeducation.com/mstm/physics/w

aves/interference/waveInterference2/WaveInt

erference2.html

82

Check Your Understanding

• Which points will produce constructive interference and

which will produce destructive interference?

Constructive

G, J, M, N

Destructive

H, I, K, L, O

• http://zonalandeducation.com/mstm/physics

/waves/interference/destructiveInterference/

InterferenceExplanation3.html

Constructive & Destructive

InterferenceWhen the two

individual

waves are

exactly in

phase the

result is large

amplitude.

When the two

gray waves

become

exactly out of

phase the sum

wave is zero.

• http://zonalandeducation.com/mstm/physics/waves

/interference/waveInterference2/WaveInterference

2.html

• http://zonalandeducation.com/mstm/physics/waves

/interference/waveInterference1/WaveInterference

1.html

• HO: Constructive & Destructive Interference

A standing wave is theresult of two wave trains of the samewavelength, frequency, and amplitude

traveling in opposite directionsthrough the same medium.

Standing Waves• A standing wave does not appear to move,

the crest and troughs appear to flip above

and below the rest position.

• They are created from positive and negative

pulses of equal shape (frequency,

wavelength and amplitude) that travel in

opposite directions.

• The point that flips from a crest to a trough

is called a loop or antinode; it is created

from constructive interference.

When the two waves are 180° out-of-phase with each other they cancel,

and when they are exactly in-phase with each other they add together. As

the two waves pass through each other, the net result alternates between

zero and some maximum amplitude. However, this pattern simply

oscillates; it does not travel to the right or the left, and thus it is called a

"standing wave".

• A standing wave is typically depicted by drawing the

shape of the medium at an instant in time and at an

instant one-half vibrational cycle later. This is done in the

diagram below.

A node is a point on the medium that is staying in the same location. An

antinode vibrates back and forth between a large upward and a large

downward displacement. Nodes and antinodes are not actually part of a

wave. Recall that a standing wave is not actually a wave but rather a

pattern that results from the interference of two or more waves. Since a

standing wave is not technically a wave, an antinode is not technically a

point on a wave. The nodes and antinodes are merely unique points on

the medium that make up the wave pattern.

Standing Waves• The point that remains at the rest position is

called a node or nodal point; it is created

from destructive interference.

– One node occurs every ½.

– One loop (anti-node) occurs every ½.

Sample Problems1) A standing wave interference pattern is produced in

a rope by a vibrator with a frequency of 28 Hz. If the

wavelength of the waves is 20 cm, what is the distance

between successive nodes?

Sample Problems2) The distance between the second and fifth nodes in

a standing wave is 60 cm. What is the wavelength of

the waves? What is the speed of the waves, if the

source has a frequency of 25 Hz?

Sample Problems3) What is the number of nodes in the following

diagram? The number of antinodes?

Practice Problems

(Recall: The ANSWERS are in

brackets for many of the

problems)

For question #1, please write in

the following measurement

Interference Patterns

• If two points are generating waves, the

crests and troughs will interact to produce a

two-point-source interference pattern.

• Areas of constructive interference and

destructive interference are produced.

– Crest + crest = constructive interference

– Trough + trough = constructive interference

– Crest + trough = destructive interference

Interference Contd.• Continuous lines indicate crests.

• Dashed lines indicate troughs.

• Filled-in dots indicate constructive interference (A, B).

• Open dots indicate destructive interference (C).

The thick lines represent wave crests and the thin lines represent wave

troughs. The red dots in the animation represent the antinodal positions

(constructive interference); the blue dots represent the nodal positions

(destructive interference).

1. Observe the two-point source interference pattern shown below.

Several points are marked and labeled with a letter.

Which of the labeled points are ...

a. ... on nodal lines?

b. ... on antinodal lines?

c. ... formed as the result of constructive interference?

d. ... formed as the result of destructive interference?

Practice Problems

The End