 # WAVES.

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WAVES

What is a wave (continuous wave)?
A repeating and periodic disturbance that transfers energy from one place to another They are an energy transport system WAVES TRANSPORT ENERGY NOT MATTER!!!

The particles in a wave vibrate however they do NOT move along with the wave, only the wave front itself moves on.

What is a pulse? A pulse is a single non repeated disturbance

How many kinds of waves can you think of?
Categorize on a ability/inability to transfer energy through a vacuum. Does the wave require a medium to transfer energy? Categorize on direction of particle movement

Categorize on a ability/inability to transfer energy through a vacuum
(Non Mechanical) Electromagnetic waves are able to transmit energy through a vacuum as well as solids, liquids, and gases. Since they are able to move through a vacuum, they do not need vibrating particles to transmit energy. They can travel through space: NO medium required

Examples of electromagnetic waves include
cosmic, gamma, x-ray, ultraviolet, visible light, infrared, microwave, radio All waves on the EM Spectrum

Categorize on a ability/inability to transfer energy through a vacuum
Mechanical waves can be transmitted through solids, liquids, and gases. Mechanical waves do need vibrating particles to transmit energy. Mechanical waves require a medium, they can not travel through space

Examples of mechanical waves include: sound waves and water waves.

Categorize on direction of particle movement
Longitudinal Transverse Surface

3 Types of Wave Motion Longitudinal and Transverse WaveMotion
Compressional (Longitudinal) Surface Waves

Motion of Molecules Direction of Wave
Transverse Waves Motion of Molecules Direction of Wave Vibration is perpendicular (up & down) to the direction the wave is moving ex. light waves, snakey

Transverse Wave Diagrams
Draw a transverse wave large enough to label 6 parts .

Transverse Waves: Anatomy
Nodal Line: equilibrium position ; its original resting position

TW Cont’d Crest: point of maximum displacement upward from the resting position Trough: point of maximum displacement downward from the resting position

TW Cont’d A wavelength: the distance from one point on a wave to the identical point on the next consecutive wave, for example, from crest to crest or trough to trough.

TW Cont’d Amplitude: the amount of maximum displacement of the wave, in other words the distance from the crest to the nodal line (resting position) or from the trough to the nodal line. Amplitude is determined by the energy put into the vibration or the work done to create the vibration. The greater the energy content of the wave, the greater the amplitude.

TW Cont’d Node: a point midway between a crest and a trough in which the particle is at the original resting position. Connecting the nodes along a wave would define the nodal line or the original resting position. Antinode: Crest or trough, point of maximum displacement

2/3 Goal: Identify parts of a longitudinal wave, apply wave formula to calculations
If you were absent yesterday, pick up Waves WS II from mailbox. This will be due tomorrow. You will want to get yesterday’s notes from another student or from my website. Review: A student with a mass of 55 kg walks up a ramp that is 10m long and 5m high. The effort exerted by the student is 325N. Identify the Fe, Fr, De, and Dr.

Cont’d crest trough wavelength amplitude

Longitudinal (Compressional) Waves
vibration is parallel to the direction of the wave. These waves require a medium (such as air or water) through which to travel. ex. Sound waves (looks like a spring) Direction of Movement Direction of Wave

Cont’d Rarefaction Compression Wavelength

Longitudinal Waves: Anatomy
Rarefaction: region in which the particles are spread out Compression: region in which the particles are close together A wavelength: composed of a complete rarefaction and a complete compression.

Surface Waves Particles in the medium travel in a circular motion compared to the direction of the wave (Waves traveling within depths of ocean are longitudinal)

common characteristics of all waves
Frequency and period are inversely related. T=1/f

T=1/f A sonar signal has a frequency of 4 * 106 Hz , what is it’s period? Answer: 2.5 * 10-7 seconds

common characteristics of all waves
The frequency of a wave is inversely related to the wavelength (λ), hence, as f increases, λ decreases. Frequency is measured in Hertz. A Hertz is sec-1.

v = f Where v = wave speed in m/s f = frequency in Hz
 = the wavelength in meters.

IMPORTANT The speed of the wave however depends solely on the medium through which a wave is traveling

Sample problem for speed
A tuning fork with a frequency of 583 Hz is vibrated, generating a sound wave. Measurements indicate that the wavelength of the sound wave being generated by the tuning fork is 0.59 m long. Calculate the speed of sound in air using this information.

A sound wave of wavelength 0
A sound wave of wavelength 0.6 m and velocity 330 m/s is produced for 0.5 seconds. What is the frequency of the wave? Answer: 550 Hz

Sample A sound wave travels 94.6m in seconds. What is the velocity of the wave? Use v = d/t 332 m/s

The frequency of the wave is determined by the motion of the vibration of the source and the speed of a wave changes when it moves from one medium to another, therefore, the wavelength must change in response when the wave moves into a different medium. The equation v=d/t can also be applied.

Wave Behavior Reflection/Waves at Boundaries Refraction Diffraction
Superposition Interference Continuous Waves Standing Waves

Waves at Boundaries Remember speed of a wave depends on:
the medium the wave is passing through not the energy that created the vibrations. Energy only determines amplitude

What is a reflection?

Reflection (2 dimensions)
Reflection is the bouncing back of a wave at a boundary. The law of reflection states that the angle between the incident ray and the normal is equal to the angle between the reflected ray and the normal. Ө1 = Ө 2

Terms Incident wave: the wave that strikes a boundary
Reflected waves: the returning wave Normal: line drawn perpendicular to surface (Reference)

Law of Reflection

Does reflection just apply to lights and mirrors?

Reflection A reflected sound wave is called an echo.
The wave equation v = f as well as the equation v = d/t can both be used for sound waves.

Wave behavior at a boundary between 2 media
Effect dependent on media’s density At boundary wave will be partially transmitted and partially reflected dependent on difference in the media This obeys conservation of energy

Free end (Dense to less Dense)
At a free or loose end boundary (going from a denser to a less dense substance) the majority of the wave is transmitted and a small amount is reflected in phase (displacement is in the same direction).

Closed end (less Dense to more Dense)
At a rigid boundary (going from a less dense to a denser substance) the majority of the wave is reflected out of phase (inverted, displacement is in the opposite direction) and a small amount is transmitted.

Why does the reflected wave have a smaller amplitude?
Energy has been lost

The boundary behavior of waves in can be summarized by the following principles:
The reflected pulse becomes inverted when a wave in a less dense medium is heading towards a boundary with a more dense medium. The amplitude of the incident pulse is always greater than the amplitude of the reflected pulse.

What is Refraction?

Refraction Refraction is the change in direction of a wave at a boundary as it passes from one medium to another due to the change in wave speed. The speed changes however the frequency stays the same. This means that the wavelength must change.

Refraction Air Glass Air fast Glass slow, wave length gets smaller

Free end (Dense to less Dense)

Closed end (less Dense to more Dense)

Looking at speeds in ropes helps us understand the next behavior

Refraction cont As a wave passes from a more dense substance to a less dense substance, its speed increases and it bends away from the normal. As a wave passes from a less dense medium to a denser medium, its speed decreases and it bends towards the normal.

AWAY FAST GAS TOWARDS SLOW SOLID

The answer is NOT 0.16 Hz Why Not?
The waves in the diagram below occurred during a time period of 6.26 s. What is the frequency? The answer is NOT 0.16 Hz Why Not?

The waves in the diagram below occurred during a time period of 6.26 s. What is the frequency?
A period is the time it takes to complete one cycle. How many cycles are shown? Therefore the period is 6.26s/3 or The Frequency can then be calculated Frequency is equal to Hz

Superposition & Wave Behavior
Wave interference Diffraction Standing waves

Waves Move in a radial pattern from point of disturbance

Interference the result of the superposition of two or more waves, i.e. two or more waves occupy the same place at the same time.

constructive vs. destructive interference
Interference can be either constructive (build) or destructive (cancel). Depends on how the waves overlap

Constructive interference
waves align in sync or in phase displacement is in same direction Resultant wave has greater amplitude than orignal waves .

Destructive interference
waves are out of sync(out of phase) displacement is in opposite direction Resultant wave has smaller amplitude than orignal waves Total destruction if waves of equal amplitudes meet 180O out of phase

constructive vs. destructive interference
According to superposition, the displacement of the medium caused by two or more waves is the algebraic sum of the displacements caused by the individual waves. If an wave with an amplitude of +8cm has constructive interference with a wave with an amplitude of +6cm, the resulting amplitude is +14cm

What represents crests? Troughs?

What is Diffraction?

Diffraction Diffraction is the bending or spreading of a wave around a barrier.

Diffraction

Double Slit Diffraction
Results in constructive and destructive interference

node vs antinode node: a point in a medium that is completely undisturbed when a wave passes. Antinode: the point of maximum displacement; it can be either a crest or a trough

Standing Wave: A result of interference
Created when two periodic waves of equal amplitude and wavelength travel in the opposite direction. the nodes and antinodes of a wave are in a constant position. as the frequency of the wave increases, the number of nodes and antinodes increases in the same amount of space.

Cont’d