Waves

Definitions of Waves A wave is a traveling that

carries through space and matter without transferring . Transverse Wave: A wave in which the

disturbance occurs to the direction of travel.

• A type of transverse wave is Longitudinal Wave: A wave in which the

disturbance occurs to the direction of travel of the wave.

• A type of longitudinal wave is Surface Wave: A wave that has charact-

eristics of both and waves.

Types of Waves

Mechanical Waves: Require a such as

, , of a spring or the fabric of a rope. Electromagnetic Waves:

can travel in the absence of a medium.

Transverse Wave Characteristics Crest: . Trough: . Amplitude:

(undisturbed position).

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Transverse Wave Characteristics (cont.)

Frequency(f): The number of the wave makes in

The unit for frequency is

Wavelength(): The minimum at which the wave repeats the

same pattern A single oscillation is also called a The units for wavelength are

Transverse Wave Characteristics (cont.)

Velocity (v): of the wave Measured in

The formula to calculate the speed of a wave is

Period (T): it takes for the wave to complete one The units for period is The formula to calculate the period is

Transverse vs. Longitudinal Waves

The Relationships v = f

The of a wave is determined by the in which it travels.

That means that for a given medium

• and are inversely proportional.

• As one , the other

Wavelength

Frequency

The Inverse RelationshipsT =

As the period , the .

Period

Frequency

Speed of a Wave on a String For a stretched rope or string:

Where: = Tension = linear density =

As the tension , the speed . As the mass , the speed . This phenomena is commonly seen in

v =

Waves at Boundaries A wave incident upon a

fixed boundary will have its reflected back in the opposite direction. Note that the wave pulse is

after reflecting off the boundary.

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Interference

occurs whenever two waves occupy the same space at the same time. Law of :

When two or more waves are present at the same time at the same place, the

disturbance is equal to the of the disturbances from the individual waves.

Wave Interference

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Interference – Process by which two waves meet producing a net

amplitude.

Wave Interference

Interference – Process by which two waves meet

out each other.

Waves

Wave: An interference pattern resulting from two waves moving in directions with the same and

such that they develop a consistent repeating pattern of

and interference.

Waves

Node: The part of a standing wave where interference is at all times ( o out of phase).

Antinode: The part of the wave where interference is maximized

( ).

Waves When a wave impacts a boundary, some

of the energy is , while some passes , or may be

. The wave that passes through is called a

wave. A wave that is transmitted through a

boundary will lose some of its energy. Electromagnetic radiation will both

down and have a wavelength when going into a denser

media. Sound will when

transitioning into a denser media.

Incident + Reflected Wave

Higher speed

Longer wavelength

Lower speed

Shorter wavelength

Transmitted Wave

Continuous Waves – Higher Speed to Lower Speed Note the differences in wavelength and amplitude between

of the wave in the two different mediums

Displacement

Boundary

v1 v2-v1

Note: This phenomena is seen with light traveling from air to water.

The Wave Equation waves can be

represented by the following equation.

y(x,t) = ymsin(t - x) Where:

ym = = (2/)x = = (2f)t =

Note that the sum (t - x) is in , not degrees.

+x

The Wave Equation

y(x,t) = ymsin(t - x)

= 2/

Waveformrepeats itself every .

= 2f

Waveformtravels through 1

(T) every . A phase constant () can be included in the phase that represents

all waves that do not pass through the origin.

The Wave Equation – An Alternate Representation

y(x,t) = ymsin(t - x)

Substituting for (2f), (2/) and ym (A) yields:

y(x,t) = Asin2(ft - x)or

y(x,t) = Asin2(vt - x)

1

Key Ideas Waves transfer without transferring

. Longitudinal waves like that of sound require a

. Transverse waves such as electro-magnetic

radiation (light) do not require a . In transverse waves, displacement is

to the direction of the wave while in longitudinal waves, the displacement is

.

Key Ideas Waves can with one

another resulting in or interference.

waves are a special case of constructive and destructive interference for two waves moving in opposite directions with the same

, and .