# Waves.

## Presentation on theme: "Waves."— Presentation transcript:

Waves

A wave is a vibratory disturbance that propagates through a medium (body of matter) or field.
Examples of waves: sound, light, water waves, microwaves.

Waves and Energy Transfer
Waves transfer energy from one place to another by repeated small vibrations of particles. Waves ONLY transfer energy NOT mass. Notice that all the matter is in the same place after the wave has passed.

Wave Types Mechanical Waves: need a medium to travel through (air or water). Sounds waves Water waves

Wave Types 2. Electromagnetic Waves: do not need a medium to travel through and can travel through a vacuum. Radio waves Light waves

Types of Wave Motion Longitudinal Wave: a wave in which the motion of the vibration is parallel to the direction of wave travel. Ex. Sound waves, compression waves in a spring, and earthquake P-waves.

Direction of wave motion
Source Of Sound Wave This is how energy is transferred for a sound wave. Notice the individual particles remain in the same location after the wave passes by. Also notice that the direction of motion of the wave and the direction of particle motion is parallel to each other.

This is how energy is transferred by compressing a spring or slinky.

This is how energy is transferred through the earth with an
earthquake P-wave. Notice the black square, it starts and ends in the same location showing us how waves transfer energy NOT matter.

Types of Wave Motion Transverse Wave: a wave in which the motion of the vibration is perpendicular to the direction of wave travel. Particle Motion Wave Motion Ex. Electromagnetic waves (light), earthquake S-waves.

This is how energy is transferred in a transverse wave.
Particle Motion Wave Motion This is how energy is transferred in a transverse wave. Fix your eye on one of the particles. Notice it’s movement as the wave passes by. It moves up, then down, then back up again. This movement is perpendicular to the wave motion.

This is how energy is transferred through the earth with an
earthquake S-wave. Notice the black square, it moves up, then down, then back up to it’s original position showing us that only energy is transferred NOT matter.

Unlike longitudinal waves, transverse waves can be oriented in many different planes.

Pulses vs. Periodic Waves
A pulse is a single short disturbance or wave that moves from one place to another. The speed of the pulse depends on the medium.

If a rope with a traveling pulse is attached to a fixed unyielding object, like a wall in the picture below, the pulse will be reflected. Reflection is the rebounding of a pulse or wave as it strikes a barrier.

What specifically happens to the pulse when it hits the wall?
Remember Newton’s 3rd Law? When the pulse arrives at the wall it exerts an upward force on the wall. The wall then exerts a force that is equal in magnitude (size of the wave doesn’t change) but opposite in direction. This reaction inverts the pulse.

As a pulse reaches a new medium, part of the pulse is transmitted through the medium, part is absorbed, and part is reflected back towards the source. Low Density Medium to High Density Medium Reflected wave is inverted, transmitted wave is slower.

High Density Medium to Low Density Medium
Reflected wave is upright, transmitted wave is faster.

A periodic wave is a series of pulses or evenly timed disturbances.

Characteristics of Periodic Waves
The complete series of changes (one complete vibration) at one point in a medium as a wave passes is called a cycle. Here particles move forward and then back as the wave passes. This forward-back motion is one cycle.

Here particles move up, down, then back to it’s original
position as the wave passes. This up-down-up motion is one cycle.

Frequency (f): # of cycles per second
A frequency of 1 cycle per second is called 1 hertz (Hz). 1 Hz = 1 s

Sound Waves and Frequency
The frequency of a sound wave determines the pitch.

Light Waves and Frequency
The frequency of a light wave determines its color.

Try this… f = 10 cycles 5 seconds = 2 cycles 1 second = 2 Hz
10 wave cycles pass a fixed point in a medium in 5 seconds. What is the frequency (cycles per second) of the wave? f = 10 cycles 5 seconds = 2 cycles 1 second = 2 Hz

Frequency of the Human Ear
Humans can detect frequencies in the range of 20 to 20,000 Hz. How does the human ear work?

The frequency tells us how many cycles per second travel through a medium. Sometimes we just want to know the time it takes to complete only 1 cycle. This is the period (T) of a wave. T = 1 f

Try this… The frequency of a wave is 2 hertz. What is the period of the wave? T = 1 f = 1 2 Hz = .5 s It takes .5 s for one complete wave cycle to pass by a point in a medium.

Try this… The frequency of a light wave is 5.0 x 1014 hertz. What is the period of the wave? T = 1 f = 5.0 x 1014 Hz = 2.0 x s

Which wave has the longest period (would take the longest time for one cycle to pass)?

Amplitude: height of a wave

The amplitude of a wave shows the amount of energy in a wave.
With sound waves amplitude is represented by loudness. Sound waves with large amplitudes are loud. With light waves amplitude is represented by brightness. Light waves with large amplitudes are brighter.

More wave characteristics:
wavelength /condensations

Wavelength (λ) Longitudinal Transverse
A wavelength is the distance between any two successive points in the same position on a wave. It’s the length of one complete wave cycle. λ λ Longitudinal Transverse

What is the λ of the wave train below?
5 m 2.5 waves = 2 m

Find the amplitude and λ for the series of waves below.
Amplitude = .1 m

Wave Phase Certain parts of a single wave have a phase associated with it. Let’s start by looking at a circle: 90° 180° 360° 270°

Points on successive waves that are in the same position on the wave (360° apart or 1 wavelength apart) are said to be “in phase.” 360°/λ

Which two points are in phase with each other?
C and F

Which 2 points are 180° out of phase?
1 λ 2 B and D, or E and G

Immediately after the wave moves through point A , will point B move up, down, left, or right?
Before you answer any question like this make sure you re-draw the wave after it has moved. B A B would move up

Speed of Waves v = fλ λ = v f Inverse relationship- if a
From this equation what is the relationship between frequency and wavelength? λ = v f Inverse relationship- if a wave has a high frequency then it is going to have a small or short wavelength.

Find the velocity of the wave below if it has a frequency of 40 Hz.
v = fλ v = 40 Hz(1.5 m) v = 60 m/s

The speed of a wave depends upon its type and
the medium through which it travels.

Sound vs. Light Waves Speed of Sound – 331 m/s (3.31 x 102 m/s)
Remember sound and light waves are different types of waves. Sound – longitudinal. Light – transverse. Therefore they travel differently and at different speeds. Speed of Sound – 331 m/s (3.31 x 102 m/s) Speed of Light – 300,000,000 m/s (3.00 x 108 m/s) Light is 1 million times faster than sound!

This is why you “see” lightning before you “hear” it.
You can approximate the storms distance in miles by counting the seconds between the lightning and thunder. Every 5 seconds is approximately 1 mile.

and arrives before the sound does.
When a source, this time something like a fighter jet, travels at a speed greater than the speed of sound, it actually outruns the sound waves, and is said to break the sound barrier, and arrives before the sound does.

Try this… The following diagram shows a segment of a periodic wave in a rope traveling to the right to point G. What type of wave is represented in the diagram? What is the amplitude of the wave? What is the wavelength of the wave? If the frequency of the wave is 2 Hz, what is the period of the wave? Determine the speed of the wave. Name the two points on the wave that are in phase. Immediately after the wave moves through point g, will point B move up, down, left, or right? 2.4 m 6.0 m

Wave Fronts In a 3-dimensional medium such as air, waves radiate in concentric spheres from a vibration point. Wavefronts/Crests Troughs

TOP VIEW SIDE VIEW

Doppler Effect When wave fronts are in motion observers will find an APPARENT change in frequency of the wave. Remember how frequency is represented in a sound wave? PITCH Remember how frequency is represented in a light wave? COLOR

Let’s take a closer look:
A wave source not in motion will radiate waves out in all directions equally. If the source of the wave is approaching an observer (or the observer is approaching the wave source) the frequency APPEARS to increase. An ambulance, with it’s siren on, is a moving source of sound waves. Notice now that the wave fronts are not equally spaced. The waves toward the front of the ambulance where the observer is appear closer together this means they appear to have a HIGHER FREQUENCY/SHORTER WAVELENGTH. HIGHER FREQUENCY EQUATES TO A HIGHER PITCHED SIREN.

If the source of the wave is leaving an observer (or the observer is leaving the wave source) the frequency APPEARS to decrease. The waves toward the back of the ambulance where the observer is appear further apart. This means they appear to have a LOWER FREQUENCY/LONGER WAVELENGTH. LOWER FREQUENCY EQUATES TO A LOWER PITCHED SIREN.

So as an ambulance approaches and then passes you the sound of the ambulance’s siren drops in pitch.

The effects are similar with light waves except we don’t hear the effects we see them.
BLUE-SHIFT RED-SHIFT A light source approaching you appears to have a higher frequency/ shorter wavelength and will appear blue in color. A light source moving away from you appears to have a lower frequency/ longer wavelength and will appear red in color.

Applications of the Doppler Effect
Weather Forecasting: Radar bounces radio waves off water particles in clouds. A computer measures how long it takes for the waves to reflect back and then uses the time to calculate how far the particle is away from the radar. Doppler radar can also calculate if a raindrop is moving toward or away from the radar. Meteorologists know that if the rain is moving, then the wind must be pushing it. That's how they can tell where the wind is blowing in clouds.

Applications of the Doppler Effect:
Radar Gun: When radio waves emitted from a radar gun hit an object that is moving toward the patrol vehicle, the returning frequency will be higher than the original. When the signal hits that vehicle that is moving away from the observer, the returning frequency will be lower than the original one. The frequency change can be used to determine the speed of the target vehicle.

Which letter is this object moving toward?

Interference: effect produced by two waves passing simultaneously through a region. What happens when waves interfere with each other? The principle of superposition states that the combined displacement of the two interfering waves is the algebraic sum.

Constructive Interference
The combination of two waves in the same phase.

2A

Destructive Interference
The combination of two waves that are 180° out of phase.

What will the amplitude of the resultant wave be when wave A and B meet at point X?

What is the amplitude of the wave produced when these waves overlap?

Wave fronts and Constructive/Destructive Interference
Here 2 crests/troughs are coming together = maximum constructive interference Wave fronts/crests Here a trough and a crest are coming together = maximum destructive interference troughs

All along here there is max constructive interference
All along here there is max destructive interference- there is no effect from either wave Wave tank

Standing Waves When two waves having the same amplitude and frequency travel in opposite directions a standing wave is formed.

Antinodes- the points of maximum displacement
when two waves are interacting. Nodes- the points of zero displacement when two waves are interacting.

The nodes and antinodes are stationary and the wave appears to stand still.

5 4 2 How many nodes are on this standing wave?
How many antinodes are on this standing wave? How many waves make up this standing wave? 2

How many wavelengths for each of these standing waves?
½ λ 1 λ 1 ½ λ 2 λ 2 ½ λ 3 λ 3 ½ λ

How many wavelengths make up this standing wave. How many nodes
How many wavelengths make up this standing wave? How many nodes? How many antinodes?

Resonance Natural Frequency- every elastic object has a particular frequency at which it will vibrate at if struck. If we strike a tuning fork to make it vibrate at its natural frequency of 512 Hz, then place it near an identical nonvibrating tuning fork, the nonvibrating tuning fork will resonate due to the vibration. This is REASONANCE.

Opera Singer shattering glass? Really?
Just like the tuning fork, a glass has a natural frequency at which it will vibrate. It is possible for an opera singer to shatter a glass by maintaining a note with a frequency equal to the natural frequency of the glass.

The transfer of energy by resonance increases the amplitude of vibrations in the glass until its structural strength is exceeded.

Tacoma Narrows Bridge, 1940 High winds set up standing waves in the bridge in addition to vibrations in a torsional (twisting) mode. Resonance increased the amplitude of vibrations until the bridge collapsed.

Diffraction Diffraction is the spreading out of a wave into a region beyond an obstacle.

The wavelength of these waves… …is the same as the wavelength of these waves.

The amount of diffraction depends on the wavelength and size of opening.
Ripple Tank

Which size slit will cause a wave to diffract the most?

Single Slit Diffraction

Double Slit Diffraction- if we use light waves we will see a pattern (fringes) appear on a nearby screen.

Not the pattern you might expect…this shows
us INTERFERENCE again.

Because the waves emanating from the two slits were originally from the same source, they always keep in step with each other. At the screen this results in bands of light where reinforcement is occurring and dark where cancellation is occurring. These bands or 'fringes' are called a diffraction pattern. The distance between the fringes y = λD/a where λ = the wavelength of the light, D = the distance from the slits to the screen and 'a' = the distance between the slits.