Wave Motion

What’s the first thing that comes to mind when you hear the word “wave”? We often think of common forms of waves such as the waves in the ocean. But there are many kinds of waves. Waves are all around us and we encounter them everyday. There are light waves, sound waves, and many more. In this section, we are going to look at common types of waves, what parts make up those waves, and real life examples of waves.

Introduction to Waves

Amplitude is a measurement from equilibrium to the crest of a wave. Equilibrium is the point half way in

between a crest and a trough in the vertical direction. We measure to the crest instead of the trough because then the amplitude is a positive number. Amplitude is a

measure of the intensity of a wave. The symbol for amplitude is A and

it is measured in meters.

Amplitude

The wavelength is the length of one complete

wave, or cycle. It is measured from crest to crest or from trough to

trough for transverse waves. It is

similar for longitudinal waves as well. The symbol for wavelength is the Greek letter lambda

(λ) and is measured in meters.

Wavelength

Period Period is the time it takes

to complete one full cycle of a wave. A cycle is

from rarefaction to rarefaction or from

compression to compression for

longitudinal waves. It is similar for

transverse waves as well. The symbol for period is T and it is measured in

seconds.

Frequency is the number of cycles that occur for every unit of

time. There are two equations for frequency. These are used to make calculations with waves.

The symbol for frequency if f and it is

measured in cycles per second.

Frequency

f = ─T1

f = ─vλ

Frequency is the inverse of period:

Frequency is equal to the velocity ofa wave divided by the wavelength:

The crest is the highest point in the vertical

direction for a transverse wave.

Similarly, the trough is the lowest point in the

vertical direction.

Crests and Troughs

The compression of a longitudinal wave is the part of the wave where the particles in a wave

are most dense. Rarefaction is the part of the wave where the

particles are least dense.

Compression and Rarefaction

There are many types of waves. In this section, we’re specifically going to look at

transverse waves and longitudinal waves, as well as

examine a special type of wave called a standing wave. They are examples of mechanical

waves. An important concept about wave motion is that

waves transfer energy, NOT matter.

Types of Waves

A transverse wave is characterized by particle

motion that is perpendicular to the

wave energy. It is important to understand

that an individual particles do not move

from there original position on the horizontal axis, they merely oscillate

vertically.

Transverse Waves

Click on the picture to visit a websitethat let’s you adjust the wavelengthand amplitude of a transverse wave.

A longitudinal wave is characterized by

particle motion that is parallel to the direction

of the wave energy. Even though they are in the same direction, it is important to note that

a particle does not move with the wave, it merely oscillates in the

same direction.

Longitudinal Waves

Click on the picture to visit a websitethat shows animated pictures of wavemotion.

The simplest type of wave is the one in which the particles of the medium are set into simple harmonic vibrations as the wave passes through it. The wave is then called a simple harmonic wave.Consider a particle O in the medium. The displacement at any instant of time is given by

Where A is the amplitude, w is the angular frequency of the wave. Consider a particle P at a distance x from the particle O on its right. Let the wave travel with a velocity v from left to right. Since it takes some time for the disturbance to reach P, its displacement can be written as

Where f is the phase difference between the particles O and P.We know that a path difference of l corresponds to a phase difference of 2p radians. Hence a path difference of x corresponds to a phase difference of  2π x

ʎ

Substituting equation (1.5) in equation (1.4)We get,

       

                                                                                                                                                                                                                                                                                                                                                                       

    Similarly, for a particle at a distance x to the left of 0, the equation for the displacement is given by

                                                                                                          

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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.

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Fixed End

• One type of boundary that a wave may encounter is that it may be attached to a fixed end.

• 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?

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Fixed End

• Here the incident pulse is an upward pulse.• The reflected pulse is upside-down. It is

inverted.• The reflected pulse has the same speed,

wavelength, and amplitude as the incident pulse.

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Fixed End Animation

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Free End

• 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?

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Free End

• Here the reflected pulse is not inverted.• 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.

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Free End Animation

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Change in Medium

• Our third boundary condition is when the medium of a wave changes.

• Think of a thin 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?

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Change in Medium

• In this situation part of the wave is reflected, and part of the wave is transmitted.

• Part of the wave energy is transferred to the more dense medium, and part is reflected.

• The transmitted pulse is upright, while the reflected pulse is inverted.

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Change in Medium

• The speed and wavelength of the reflected wave remain the same, but the amplitude decreases.

• The speed, wavelength, and amplitude of the transmitted pulse are all smaller than in the incident pulse.

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Change in Medium Animation

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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.

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Constructive Interference

• Let’s consider two waves moving towards each other, both having a positive upward amplitude.

• What will happen when they meet?

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Constructive Interference• They will ADD together to produce a

greater amplitude.• This is known as CONSTRUCTIVE

INTERFERENCE.

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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?

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Destructive Interference• This time when they add together they

will produce a smaller amplitude.• This is know as DESTRUCTIVE

INTERFERENCE.

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Check Your Understanding

• Which points will produce constructive interference and which will produce destructive interference?

Constructive G, J, M, N

Destructive H, I, K, L, O

Quickne tube Experiment