# Waves are everywhere in nature

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Waves are everywhere in nature
Sound waves, visible light waves, radio waves, microwaves, water waves, sine waves, telephone chord waves, stadium waves, earthquake waves, waves on a string, slinky waves

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

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.

Period (T) - the shortest time interval during
Frequency (f)- the number of complete cycles per unit time f = cycles time measured in units of Hz (s-1) Eg. Five crests pass a point every second so f = 5 cycles/s = 5 Hz Period (T) - the shortest time interval during which the motion repeats itself T = time cycle measured in units of time (s, min) Eg. A pendulum bob takes 3.5 s to swoing “to and fro” f = 1/T T = 1/f &

Sample Problems e.g. A child on a swing completes 20 cycles in 25 s. Calculate the frequency and the period of the swing. e.g. A stroboscope is flashing so that the time interval between flashes is 1/80 s. Calculate the frequency of the stobe light’s flashes. e.g. Calculate the frequency and the period of a tuning fork that vibrates times in 1.00 min. Page 10 #1 – 4, page 17 #8 - 13

A single disturbance is called a pulse or shock wave
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.

TRANSVERSE The displacement of the particles
of the medium is perpendicular to the direction of wave propagation (pulse). 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!

LONGITUDINAL The 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

Anatomy of a Wave crest The points A and F are called the CRESTS of the wave. This is the point where the wave exhibits the maximum amount of positive or upwards displacement

Anatomy of a Wave trough 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.

Anatomy of a Wave cont. Amplitude 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.

Anatomy of a Wave cont. wavelength 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 is can a wavelength be measured?

Recall: The distance between two consecutive similar points is called the wavelength (λ).

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.

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. measure the λ; b. measure 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: p. 17 – 18 #2, 3, 14, 16

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

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: (in handout) 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? 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? Practice: p. 15 #1-6; p #15, 17-32

Wave Behavior We know that waves travel through mediums.
But what happens when that medium runs out?

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.

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?

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.

Fixed End Animation

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?

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.

Free End Animation

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?

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

Less Dense to More Dense Medium

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?

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

Change in Medium Animation

Sample Problems A negative pulse is sent along a spring. The spring is attached to a light thread that is tied to the wall.  Describe the speed and type of pulse that is transmitted at A. Describe the speed and type of pulse that is reflected at A. Describe the speed and type of pulse that is reflected at B. 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? 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: p. 17 #4 LM: p. 3 - Reflection at Barriers

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.

If the wavefront 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.

Sample Problems The diagram shows wave fronts striking a barrier.
Draw the incident direction. Draw the normal. Measure the angle of incidence. Draw the reflected direction. Draw the reflected wave fronts.

2. The diagram shows the direction of a wave that strikes a curved barrier.
Draw the tangent line. Draw the normal. Measure the angle of incidence. Draw the reflected direction. Draw the reflected wave fronts.

HO: Drawing & Measuring Waves

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.

Constructive Interference
Let’s consider two waves moving towards each other, both having a positive upward amplitude. What will happen when they meet?

Principle of Superposition
Interference the result of the superposition of two or more waves Principle of Superposition the displacement of the medium when two or more waves pass through it at the same time is the algebraic sum of the displacements caused by the individual waves

Constructive Interference
Let’s consider two waves moving towards each other, both having a positive upward amplitude. What will happen when they meet?

Constructive Interference
They will ADD together to produce a greater amplitude. This is known as CONSTRUCTIVE INTERFERENCE.

Constructive Interference

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?

Destructive Interference
This time when they add together they will produce a smaller amplitude. This is know as DESTRUCTIVE INTERFERENCE.

Which points will produce constructive interference and which will produce destructive interference? Constructive G, J, M, N Destructive H, I, K, L, O

Constructive & Destructive Interference
When 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.

HO: Constructive & Destructive Interference

Constructive & Destructive Waves Handout
(Practice page 19 #33-34; p. 35 #35 – 37)

result of two wave trains of the same
A standing wave is the result of two wave trains of the same wavelength, frequency, and amplitude traveling in opposite directions through 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. An antinode 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 Problems 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? 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? Practice: LM p. 4 - Standing Waves; p. 17 #7, p. 36 #38-43

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
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?

e. g. Draw a two-point-source interference pattern
e.g. Draw a two-point-source interference pattern. The sources are 2 cm apart. The wavelength of each source is 1 cm.

Practice: LM p. 6 - Interference Patterns;

The End

ELECTROMAGNETIC waves.
No medium is needed for ELECTROMAGNETIC waves. Light, radio, x-rays, and gamma rays are some examples of e/m waves. All e/m waves travel through free space at a speed of approximately 3.00 x 108 m/s or 186,000 miles/sec. This speed is known as the speed of light.

Click here to view a simulation of the interference of two traveling waves that can result in a standing wave. Click here to view a simulation of standing waves on a string. Standing waves may be produced easily in water, string, and air columns.

the maximum displacement of a particle of the medium from
Amplitude the maximum displacement of a particle of the medium from the rest or equilibrium position denoted by A and measured in units of length

the shortest distance between two points that are “in phase”
Wavelength the shortest distance between two points that are “in phase” denoted by l and measured in units of length

v = d/t = l/T = f l Velocity - the speed of the wave
denoted by v and measured in units of dist/time The speed of a wave depends on the properties of the medium through which it is traveling. v = d/t = l/T = f l

Reflection the turning back of a wave when
it reaches the boundary of the medium through which it is traveling

the angle of incidence is equal to the angle of reflection
Law of Reflection the angle of incidence is equal to the angle of reflection

There are two types of reflection.
Fixed-end Termination the reflected wave is inverted when it reflects from a more dense medium Free-end Termination the reflected wave is upright when it reflects from a less dense medium Click here to view these types of reflection.

Refraction the bending of a wave as it passes obliquely from one medium into another of different propagation speed For refraction to occur, the wave must change speed and must enter the new medium at an oblique angle.

Diffraction the spreading of a wave around a barrier or
through an opening

results in a larger amplitude results in a smaller amplitude
Types of Interference Constructive results in a larger amplitude Destructive results in a smaller amplitude

pattern resulting from the superposition of two transverse waves. Click here and here to view simulations of the interference of two circular waves.

The ripple tank simulation found here can be used to investigate
wave properties. You can view reflection, refraction, diffraction, and interference using both plane and circular waves. Click here to view a movie clip of an actual ripple tank experiment.

Doppler Effect the change in frequency due to the relative
motion of the wave source and the observer The observed frequency is higher when the source and observer are getting closer. The observed frequency is lower when the source and observer are getting farther away.