WAVES

Chapter 14

What is a Wave? A disturbance that travels through

a medium from one location to another location without transporting matter.

Each individual particle of the medium is temporarily displaced and then returns to its original equilibrium position.

equilibrium position The natural position where the

particles naturally fall, spaced equally far apart.

To introduce a wave into a medium, the first particle is displaced or moved from its equilibrium or rest position. The particle might be moved upwards or downwards, forwards or backwards; but once moved, it is returns to its original equilibrium or rest position.

PULSE

A single disturbance moving through a medium from one location to another location.

The repeating and periodic disturbance

which moves through a medium from one

location to another is referred to as a wave.

medium

A substance or material which carries the wave.

The wave medium is not the wave and it doesn't make the wave; it merely carries or transports the wave from its source to other locations.

the medium is a series of interconnected particles

The medium is composed of parts which are capable of interacting with each other. The interactions of one particle of the medium with the next adjacent particle allows the disturbance to travel through the medium.

Individual particles of the medium are only temporarily displaced from their rest position

There is always a force acting upon the particles which restores them to their original position. It is for

this reason, that a wave is said to involve the movement of a

disturbance without the movement of matter.

Any wave moving through a medium has a source. Somewhere along the medium,

there was an initial displacement of one of the particles.

Waves are an energy transport phenomenon

As a disturbance moves through a medium from one particle to its adjacent particle, energy is being transported from one end of the medium to the other.

Categories of Waves Transverse Longitudinal Surface

transverse waves a wave in which particles of the

medium move in a direction perpendicular to the direction which the wave moves.

Longitudinal Waves A wave in which particles of the

medium move in a direction parallel to the direction which the wave moves.

Surface Wave

A wave in which particles of the medium undergo a circular motion.

Only the particles at the surface of the medium which undergo the circular motion.

Comparing Transverse and Longitudinal Waves Waves traveling through a solid medium

can be either transverse waves or longitudinal waves.

Waves traveling through the bulk of a fluid (such as a liquid or a gas) are always longitudinal waves.

Transverse waves require a relatively rigid medium in order to transmit their energy.

The ability to transmit energy through a vacuumAn electromagnetic wave is a wave

which is capable of transmitting its energy through a vacuum (i.e., empty space).

A mechanical wave is a wave which is NOT capable of transmitting its energy through a vacuum. Mechanical waves require a medium in order to transport their energy from one location to another. 

The Anatomy of a Wave

1. The solid horizontal line is the equilibrium position of the string.

2. The crest is the point of maximum positive displacement. 3. The trough of a wave is the point of maximum negative

displacement.4. The amplitude is the maximum amount of vertical

displacement.5. The wavelength of a wave is the length of one complete

wave cycle.

Period and Frequency are Reciprocals A period () of a wave is equal to

the number of seconds that it takes for one cycle to pass a point.

The frequency of the wave (f) is the number of cycles that pass a point in one second.

F = 1/

Velocity is rate of change of distance

Velocity = distance / time

Velocity = wavelength / period

Wavelength, velocity and frequency

Since v = / And f = 1/

Then, v = * f

Boundary Behavior The behavior of a wave (or pulse) upon

reaching the end of a medium is referred to as boundary behavior.

When one medium ends, another medium begins; the interface of the two media is referred to as the boundary.

As a wave travels through a medium, it will often reach the end of the medium and encounter an obstacle or perhaps another medium through which it could travel.

fixed end boundary When the last particle of a medium is unable

to move. The incident pulse is the one which is

approaching the boundary. When the incident pulse reaches the boundary, two things occur: A portion of the energy carried by the pulse is

reflected and returns towards the left end of the rope. This is known as the reflected pulse.

A portion of the energy carried by the pulse is transmitted to the new medium, causing it to vibrate.

Characteristics of the reflected pulse off a fixed end boundary

The reflected pulse is inverted. The speed of the reflected pulse is the same

as the speed of the incident pulse The wavelength of the reflected pulse is the

same as the wavelength of the incident pulse

The amplitude of the reflected pulse is less than the amplitude of the incident pulse

free end boundary

When the end of the medium is free to move.

The reflected pulse is not inverted.

From a less dense to a more dense medium

A portion of the energy carried by the incident pulse is reflected and returns towards the less dense medium, and is called the reflected pulse.

A portion of the energy carried by the incident pulse is transmitted into the more dense medium, and is called the transmitted pulse.

The reflected pulse will be inverted. The transmitted pulse is not inverted.

Comparisons between the characteristics of the transmitted pulse and the reflected pulse.

particles in the more dense medium will be vibrating with the same frequency as particles in the less dense medium.

The pulse in the more dense medium travels slower than the pulse in the less dense medium. Waves always travel fastest in the least dense medium.

the pulse in the more dense medium has a smaller wavelength than the pulse in the less dense medium.

Comparison of the reflected pulse and the incident pulse. The incident and the reflected pulse share

the same medium. Since the two pulses are in the same medium, they will have the same speed.

Since the reflected pulse was created by the vibrations of the incident pulse, they will have the same frequency.

And two waves with the same speed and the same frequency, must have the same wavelength.

From more dense to less dense medium. There will be partial

reflection and partial transmission at the boundary.

The reflected pulse in this situation will not be inverted.

the transmitted pulse is not inverted (as is always the case).

A Summary of the boundary behavior of waves the wave speed is always greatest in the least

dense medium the wavelength is always greatest in the least

dense medium the frequency of a wave is not altered by

crossing a boundary 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

Reflection The wave doesn't just stop when it reaches the

end of a medium. There will be some reflection off the boundary and some transmission into the new medium.

Reflection involves a change in direction of waves when they bounce off a barrier

waves will always reflect in such a way that the angle at which they approach the barrier equals the angle at which they reflect off the barrier. This is known as the law of reflection.

Refraction refraction of waves

involves a change in the direction of waves as they pass from one medium to another.

Refraction, or bending of the path of the waves, is accompanied by a change in speed and wavelength of the waves.

Diffraction Diffraction involves a

change in direction of waves as they pass through an opening or around a barrier in their path.

the amount of diffraction increases with increasing wavelength.

Interference of Waves Wave interference is the

phenomenon which occurs when two waves meet while traveling along the same medium.

The interference of waves causes the medium to take on a shape which

results from the net effectnet effect of the two individual waves upon the particles of the medium.

constructive interference Constructive interference is a type of

interference which occurs at any location along the medium where the two interfering waves have a displacement in the same direction.

When both waves have an upward displacement, the medium has an upward displacement which is greater than the displacement of the two interfering pulses.

Constructive interference is observed when a crest meets a crest;

but it is also observed when a trough meets a trough.

Destructive Interference A type of interference

which occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction.

The result is that the two pulses destroy each other.

the medium's displacement is less than the displacement of the largest-amplitude wave.

Complete destructive interference When they are completely

overlapped, the individual waves are completely destroyed.

At the instant of complete overlap, there is no resulting disturbance in the medium.

This "destruction" is a momentary, not a permanent, condition. After two pulses pass through each

other, there is still a crest and a trough heading in the same direction which they were heading before interference.

the principle of superposition

The principle of superposition is sometimes stated as follows:

When two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location.

The Principle of Superposition

The Doppler Effect The Doppler effect is observed

whenever the source of waves is moving with respect to an observer.

The Doppler effect the effect produced by a moving source of waves in which there is an apparent upward shift in frequency for observers towards whom the source is approaching and an apparent downward shift in frequency for observers from whom the source is receding.

Traveling Waves vs. Standing Waves

Traveling waves are observed when a wave is not confined to a given space along the medium.

A traveling wave is a repeating pattern which is observed to move through a medium in uninterrupted fashion.

Waves on a Rope A wave on a rope will quickly reach the

end of a cord, reflect and travel back in the opposite direction. Any reflected portion of the wave will then interfere with the portion of the wave incident towards the fixed end. This interference produces a new shape in the medium.

Standing Waves If a rope is held end to end and vibrated at just

the right frequency, a wave pattern would be produced which assumes the shape of a sine wave and is seen to change over time.

When the proper frequency is used, the interference of the incident wave and the reflected wave occur in such a manner that there are specific points along the medium which appear to be standing still.

Because the observed wave pattern is characterized by points which appear to be standing still, the pattern is often called a standing wave pattern.

There are other points along the medium whose displacement changes over time, but in a regular manner.

These points vibrate back and forth from a positive displacement to a negative displacement.

The vibrations occur at regular time intervals such that the motion of the medium is regular and repeating - a pattern is readily observable.

Formation of Standing Waves A standing wave pattern is a

vibrational pattern created within a medium when the vibrational frequency of the source causes reflected waves from one end of the medium to interfere with incident waves from the source in such a manner that specific points along the medium appear to be standing still.

standing wave pattern Such patterns are only created within the

medium at specific frequencies of vibration; these frequencies are known as harmonic frequencies, or merely harmonics.

At any frequency other than a harmonic frequency, the interference of reflected and incident waves results in a resulting disturbance of the medium which is irregular and non-repeating.

two waves traveling in opposite directions along the same medium

The waves are interfering in such a manner that there are points of no displacement produced at the same positions along the medium, known as nodes (N).

There are also points along the medium which vibrate back and forth between points of large positive displacement and points of large negative displacement, known as antinodes (AN).

Nodes and antinodes should not be confused with crests

and troughs. When the motion of a

traveling wave is discussed, a point of large maximum displacement is a crest and a point of large negative displacement is a trough. These represent points of the disturbance which travel from one location to another through the medium.

Nodes and antinodes are points on the medium.

Nodes and antinodes are not actually part of a wave.

A standing wave is not actually a wave but rather a pattern which results from the interference of two or more waves.