PhysicsWaves

Waves and Wave Characteristics

A wave can be described as a disturbance that travels through a medium from one location to another location. Waves are said to transport energy but not matter. 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.

An electromagnetic wave is a wave which is capable of transmitting its energy through a vacuum (i.e., empty space). Electromagnetic waves like light are produced by the vibration of electrons within atoms on the Sun's surface.

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. A sound wave is an example of a mechanical wave. Sound waves are incapable of traveling through a vacuum. But what is meant by the word medium? A medium is a substance or material which carries the wave.

A transverse wave is a wave in which particles of the medium move in a direction perpendicular to the direction which the wave moves.

A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction which the wave moves. Because the vibrations move longitudinally, there are regions where the medium become pressed together and other regions where the medium is spread apart. A region where the it's pressed together in a small amount of space is known as a compression. A compression is a point on a medium through which a longitudinal wave is traveling which has the maximum density. A region where the medium is spread apart, thus maximizing the distance between vibrations, is known as a rarefaction. A rarefaction is a point on a medium through which a longitudinal wave is traveling which has the minimum density.

A surface wave is a wave in which particles of the medium undergo a circular motion. Surface waves are neither longitudinal nor transverse. In longitudinal and transverse waves, all the particles in the entire bulk of the medium move in a parallel and a perpendicular direction (respectively) relative to the direction of energy transport. In a surface wave, it is only the particles at the surface of the medium which undergo the circular motion.

A pulse is 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 traveling wave.

For us to work with waves we must be familiar with the vocabulary of wave motion. You will need to know and be able to apply the following terms:

The amplitude of a wave refers to the maximum amount of displacement of a a particle on the medium from its rest position. In a sense, the amplitude is the distance from rest to crest. Amplitude is a measure of the energy being transported by the wave. The greater the amplitude the greater the energy of the wave.

The wavelength of a wave is simply the length of one complete wave cycle. A wave has a repeating pattern. And the length of one such repetition (known as a wave cycle) is the wavelength. The wavelength can be measured as the distance from crest to crest or from trough to trough. In fact, the wavelength of a wave can be measured as the distance from a point on a wave to the corresponding point on the next cycle of the wave.

The frequency of a wave refers to how often the particles of the medium vibrate when a wave passes through the medium. Frequency is a part of our common, everyday language. For example, it is not uncommon to hear a question like "How frequently do you mow the lawn?" Of course the question is an inquiry about how often the lawn is mowed and the answer is usually given in the form of "1 time per week." In mathematical terms, the frequency is the number of complete vibrational cycles of a medium per a given amount of time. Given this definition, it is reasonable that the quantity frequency would have units of cycles/second, waves/second, vibrations/second, or something/second. Another unit for frequency is the Hertz (abbreviated Hz) where 1 Hz is equivalent to 1 cycle/second. The frequency is equal to 1/T, where T represents the period.

The period of a wave is the time for a particle on a medium to make one complete vibrational cycle. Period, being a time, is measured in units of time such as seconds, hours, days or years. This is equal to 1/f.

Wave Equation

Speed is equal to distance divided by time, so the speed of a wave can be calculated by dividing the wavelength by the period.

Since the period is the reciprocal of the frequency, the expression 1/f can be substituted into the above equation for period. Rearranging the equation yields a new equation of the form:

Speed = Wavelength * Frequency

The above equation is known as the wave equation. It states the mathematical relationship between the speed (v) of a wave and its wavelength ( ) and frequency (f). Using the symbols v, lambda , and f, the equation can be rewritten as

v = f x lambda

Speed is dependent upon the medium, not the energy of the wave. As a wave moves from one medium to another the speed will change. This mean as the velocity goes up the wavelength will decrease and as velocity goes down the wavelength goes up. Frequency will be unchanged.

Waves always travel fastest in the least dense medium. Since the wavelength of a wave depends upon the frequency and the speed, the wave with the greatest speed must also have the greatest wavelength. Any two waves with the same speed and the same frequency, must have the same wavelength.

Waves can be the result of a single pulse or can be the result of a continuos vibration. If a wave is created where the pattern doesn't move, i.e. the crest and troughs simply switch positions and the wave doesn't seem to move along the medium, this is a standing wave. In a standing wave the part of the medium that remains undisturbed is the node. The points of maximum displacement is the anti-nodes.

Behavior of reflected waves and at boundaries between different mediums.

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

The original wave under consideration is called the incident wave since it is incident towards (i.e., 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 origin of the wave. The disturbance which returns is known as the reflected pulse.

· A portion of the energy carried by the pulse is transmitted into the new medium, allowing a portion of the wave to continue in the original direction. This is the transmitted wave.

The amount reflected depends upon the two media. If a wave moves from a dense into a less dense medium the wave is mostly transmitted. If it moves from a less dense into a more dense it will be mostly reflected.

The reflected wave may change its form somewhat. If the wave moves through a material that has a fixed attachment as the medium boundary, like a rope attached to a wall, the wave will reflect inverted. That is, if a crest is incident towards a fixed end boundary, it will reflect and return as a trough. Similarly, if a trough is incident towards a fixed end boundary, it will reflect and return as a crest.

If the wave moves through a medium that is not rigidly fixed at the boundary, as a rope attached to a pole by a ring which allows the rope to move vertically. As the wave reaches the boundary the reflected wave will be upright. The ring will move up and down with the wave and the reflected wave will be transmitted exactly as the incident wave, upright.

Interference of Waves

What happens when two waves meet while they travel through the same medium? What effect will the meeting of the waves have upon the appearance of the medium? Will the two waves bounce off each other upon meeting (much like two billiard balls would) or will the two waves pass through each other? These questions involving the meeting of two or more waves along the same medium pertain to the topic of wave interference.

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 effect of the two individual waves upon the particles of the medium. To begin our exploration of wave interference, consider two pulses of the same amplitude traveling in different directions along the same medium. Let's suppose that each crest has an amplitude of +1 unit (the positive indicates an upward displacement as would be expected for a crest) and has the shape of a sine wave. As the sine crests move towards each other, there will eventually be a moment in time when they are completely overlapped. At that moment, the resulting shape of the medium would be a sine crest with an amplitude of +2 units. This type of interference is sometimes called 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. In this case, both waves have an upward displacement; consequently, 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. Constructive interference is where the waves tend to amplify each others crest and troughs.

Destructive interference is a type of interference which occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction. For instance, when a sine crest with an amplitude of +1 unit meets a sine trough with an amplitude of -1 unit, destructive interference occurs.

The interfering pulses have the same maximum displacement but in opposite directions. The result is that the two pulses completely destroy each other when they are completely overlapped. At the instant of complete overlap, there is no resulting disturbance in the medium. This "destruction" is not a permanent condition. In fact, to say that the two waves destroy each other can be partially misleading. When it is said that the two pulses "destroy each other," what is meant is that when overlapped, the effect of one of the pulses on the displacement of a given particle of the medium is "destroyed" or canceled by the effect of the other pulse. The waves simply cancel each others displacement. When two pulses with opposite displacements (i.e., a crest and trough) meet at a given location, the upward pull of the crest is balanced (canceled or "destroyed") by the downward pull of the trough. Once the 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. Destructive interference leads to only a momentary condition in which the medium's displacement is less than the displacement of the largest-amplitude wave.

Interestingly, the meeting of two waves along a medium does not alter the individual waves or even deviate them from their path. This only becomes an astounding behavior when it is compared to what happens when two billiard balls meet or two football players meet. Billiard balls might crash and bounce off each other and football players might crash and come to a stop. Yet waves meet, produce a net resulting shape of the medium, and then continue on doing what they were doing before the interference.

The task of determining the shape of the resultant demands that the principle of superposition is applied. 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."

This page was last updated on: November 6, 2001



	Waves and Wave Characteristics A wave can be described as a disturbance that travels through a medium from one location to another location. Waves are said to transport energy but not matter. 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. An electromagnetic wave is a wave which is capable of transmitting its energy through a vacuum (i.e., empty space). Electromagnetic waves like light are produced by the vibration of electrons within atoms on the Sun's surface. 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. A sound wave is an example of a mechanical wave. Sound waves are incapable of traveling through a vacuum. But what is meant by the word medium? A medium is a substance or material which carries the wave. A transverse wave is a wave in which particles of the medium move in a direction perpendicular to the direction which the wave moves. A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction which the wave moves. Because the vibrations move longitudinally, there are regions where the medium become pressed together and other regions where the medium is spread apart. A region where the it's pressed together in a small amount of space is known as a compression. A compression is a point on a medium through which a longitudinal wave is traveling which has the maximum density. A region where the medium is spread apart, thus maximizing the distance between vibrations, is known as a rarefaction. A rarefaction is a point on a medium through which a longitudinal wave is traveling which has the minimum density. A surface wave is a wave in which particles of the medium undergo a circular motion. Surface waves are neither longitudinal nor transverse. In longitudinal and transverse waves, all the particles in the entire bulk of the medium move in a parallel and a perpendicular direction (respectively) relative to the direction of energy transport. In a surface wave, it is only the particles at the surface of the medium which undergo the circular motion. A pulse is 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 traveling wave. For us to work with waves we must be familiar with the vocabulary of wave motion. You will need to know and be able to apply the following terms: The amplitude of a wave refers to the maximum amount of displacement of a a particle on the medium from its rest position. In a sense, the amplitude is the distance from rest to crest. Amplitude is a measure of the energy being transported by the wave. The greater the amplitude the greater the energy of the wave. The wavelength of a wave is simply the length of one complete wave cycle. A wave has a repeating pattern. And the length of one such repetition (known as a wave cycle) is the wavelength. The wavelength can be measured as the distance from crest to crest or from trough to trough. In fact, the wavelength of a wave can be measured as the distance from a point on a wave to the corresponding point on the next cycle of the wave. The frequency of a wave refers to how often the particles of the medium vibrate when a wave passes through the medium. Frequency is a part of our common, everyday language. For example, it is not uncommon to hear a question like "How frequently do you mow the lawn?" Of course the question is an inquiry about how often the lawn is mowed and the answer is usually given in the form of "1 time per week." In mathematical terms, the frequency is the number of complete vibrational cycles of a medium per a given amount of time. Given this definition, it is reasonable that the quantity frequency would have units of cycles/second, waves/second, vibrations/second, or something/second. Another unit for frequency is the Hertz (abbreviated Hz) where 1 Hz is equivalent to 1 cycle/second. The frequency is equal to 1/T, where T represents the period. The period of a wave is the time for a particle on a medium to make one complete vibrational cycle. Period, being a time, is measured in units of time such as seconds, hours, days or years. This is equal to 1/f. Wave Equation Speed is equal to distance divided by time, so the speed of a wave can be calculated by dividing the wavelength by the period. Since the period is the reciprocal of the frequency, the expression 1/f can be substituted into the above equation for period. Rearranging the equation yields a new equation of the form: *Speed = Wavelength Frequency The above equation is known as the wave equation. It states the mathematical relationship between the speed (v) of a wave and its wavelength ( ) and frequency (f). Using the symbols v, lambda , and f, the equation can be rewritten as v = f x lambda Speed is dependent upon the medium, not the energy of the wave. As a wave moves from one medium to another the speed will change. This mean as the velocity goes up the wavelength will decrease and as velocity goes down the wavelength goes up. Frequency will be unchanged. Waves always travel fastest in the least dense medium. Since the wavelength of a wave depends upon the frequency and the speed, the wave with the greatest speed must also have the greatest wavelength. Any two waves with the same speed and the same frequency, must have the same wavelength. Waves can be the result of a single pulse or can be the result of a continuos vibration. If a wave is created where the pattern doesn't move, i.e. the crest and troughs simply switch positions and the wave doesn't seem to move along the medium, this is a standing wave. In a standing wave the part of the medium that remains undisturbed is the node. The points of maximum displacement is the anti-nodes. Behavior of reflected waves and at boundaries between different mediums. When one medium ends and another medium begins, the interface of the two media is referred to as the boundary. The original wave under consideration is called the incident wave since it is incident towards (i.e., 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 origin of the wave. The disturbance which returns is known as the reflected pulse. · A portion of the energy carried by the pulse is transmitted into the new medium, allowing a portion of the wave to continue in the original direction. This is the transmitted wave. The amount reflected depends upon the two media. If a wave moves from a dense into a less dense medium the wave is mostly transmitted. If it moves from a less dense into a more dense it will be mostly reflected. The reflected wave may change its form somewhat. If the wave moves through a material that has a fixed attachment as the medium boundary, like a rope attached to a wall, the wave will reflect inverted. That is, if a crest is incident towards a fixed end boundary, it will reflect and return as a trough. Similarly, if a trough is incident towards a fixed end boundary, it will reflect and return as a crest. If the wave moves through a medium that is not rigidly fixed at the boundary, as a rope attached to a pole by a ring which allows the rope to move vertically. As the wave reaches the boundary the reflected wave will be upright. The ring will move up and down with the wave and the reflected wave will be transmitted exactly as the incident wave, upright. Interference of Waves What happens when two waves meet while they travel through the same medium? What effect will the meeting of the waves have upon the appearance of the medium? Will the two waves bounce off each other upon meeting (much like two billiard balls would) or will the two waves pass through each other? These questions involving the meeting of two or more waves along the same medium pertain to the topic of wave interference. 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 effect of the two individual waves upon the particles of the medium. To begin our exploration of wave interference, consider two pulses of the same amplitude traveling in different directions along the same medium. Let's suppose that each crest has an amplitude of +1 unit (the positive indicates an upward displacement as would be expected for a crest) and has the shape of a sine wave. As the sine crests move towards each other, there will eventually be a moment in time when they are completely overlapped. At that moment, the resulting shape of the medium would be a sine crest with an amplitude of +2 units. This type of interference is sometimes called 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. In this case, both waves have an upward displacement; consequently, 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. Constructive interference is where the waves tend to amplify each others crest and troughs. Destructive interference is a type of interference which occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction. For instance, when a sine crest with an amplitude of +1 unit meets a sine trough with an amplitude of -1 unit, destructive interference occurs. The interfering pulses have the same maximum displacement but in opposite directions. The result is that the two pulses completely destroy each other when they are completely overlapped. At the instant of complete overlap, there is no resulting disturbance in the medium. This "destruction" is not a permanent condition. In fact, to say that the two waves destroy each other can be partially misleading. When it is said that the two pulses "destroy each other," what is meant is that when overlapped, the effect of one of the pulses on the displacement of a given particle of the medium is "destroyed" or canceled by the effect of the other pulse. The waves simply cancel each others displacement. When two pulses with opposite displacements (i.e., a crest and trough) meet at a given location, the upward pull of the crest is balanced (canceled or "destroyed") by the downward pull of the trough. Once the 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. Destructive interference leads to only a momentary condition in which the medium's displacement is less than the displacement of the largest-amplitude wave. Interestingly, the meeting of two waves along a medium does not alter the individual waves or even deviate them from their path. This only becomes an astounding behavior when it is compared to what happens when two billiard balls meet or two football players meet. Billiard balls might crash and bounce off each other and football players might crash and come to a stop. Yet waves meet, produce a net resulting shape of the medium, and then continue on doing what they were doing before the interference. The task of determining the shape of the resultant demands that the principle of superposition** is applied. 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."





		This page was last updated on: November 6, 2001