Harrison County High School

Waves

A wave is a disturbance that carries energy through matter or space (356)

We generally discuss two types of waves:1.Mechanical2.Electromagnetic

Mechanical waves require a medium (or substance) in which to travel

Electromagnetic (EM) waves do not require a medium

Therefore, EM waves can travel through a vacuum (like space)

Recall that energy is the ability to do work……work is the movement of an object over a distance…

When an ocean wave (think of a hurricane’s waves) reach a boat, the waves move the boat (usually violently and sometimes destructively).

Since the boat moves, work is done, therefore the waves must transfer energy

Wave energy spreads out over time

V

Most waves are created by vibrations

As the energy of a wave spreads out, it creates wave fronts

As the wave fronts get larger, the energy is spread out over a larger area

Diagram 11-4 p 359

The spring pulls the mass upward when released, compresses, then pushes the mass back in the direction where is started from

If this motion can continue (forever), it is called “simple harmonic motion”

If this motion fades out over time, it is called “damped harmonic motion”

The motion of particles in a medium acts like the motion of the springs

There are three wave forms

1. Transverse waves have perpendicular motion

2. Longitudinal waves have parallel motion

3. Surface waves produce circular motion

Characteristics of a Transverse Wave

All transverse waves have similar shapes, regardless as to how big they are or what medium they travel through

An ideal transverse wave produces a shape that is represented by a sine curve

Mathematically, the sine curve is produced from the function:

f(x) = A sin

The characteristics of the transverse wave can be diagramed using the sine wave (Figure 11-9, p 365)

Crest

TroughWavelength ()

Amplitude (A)

The characteristics of a longitudinal wave can be represented by a “slinky” (Figure 1-10, p 366)

Compression Rarefaction

The amplitude (A) of a longitudinal wave is determined by the density or pressure on the medium, converted to a transverse or sine wave

Wavelength is the distance between the crests or troughs of two waves, OR the distance between compressions or rarefactions of two waves

The symbol for wavelength is the Greek character lambda (lc),

Since wavelength is a measurement of distance, the SI unit is the meter

Period (T) is the amount of time required for one full wave to pass a given point

Since period is a measurement of time, the SI unit is the second (s)

Frequency is the number of vibrations (or waves) that occur in a 1.0 s time interval

Frequency = 1 / period

f = 1 / T

The SI units for frequency is equal to 1/s, and is called a hertz (Hz)

Light is a form of Electromagnetic radiation (EMR)

EMR and the electromagnetic spectrum results from the vibration of an atom

The EM spectrum occurs in a wide range of frequencies and wavelengths

There are seven regions of the EM spectrum determined by specific frequencies and wavelengths

EM Spectrum

Increasing frequency

Increasing wavelength

Radio Micro Infrared Visible UV X-Ray Gamma

Each band of the EM spectrum has different uses or applications. See Table 11-1, p 368.

Wave Speed is the speed with which the wave is moving through a medium

Since, speed = distance / time, then:

S = wavelength (m) / period (s)

S = / T

Since frequency = 1 / T, then:

S = f

Practice, p 370, Questions 1-4

The speed of a wave depends on the medium

Kinetic theory explains the differences in wave speed (p 371)

Gases: molecules spread far apart, vibrations must travel a long ways before transferring vibration to another molecule

Waves do NOT travel fast in gases (like air)

Liquids: molecules are closer together which allow the vibrations to transfer much easier

Waves travel moderately fast in liquids (like water)

Solids: molecules are tightly packed together allowing vibrations to transfer through the entire mass of molecules almost immediately

The greater a solids density, the faster the wave speed

Waves travel extremely fast through solid (like a steel railroad track)

The wave speed of EM waves in a vacuum (e.g. light in space) is finite or constant

Light speed (c) is approximately 3.0 x 108 m/s or 186,000 miles/s

According to Einstein’s theory of general relativity, no speed can exceed the speed of light (c).

EM waves slow considerably when passing through mediums (e.g. air or water)

Doppler Effect

The pitch of a sound, how high or low it is, is determined by the frequency at which sound waves strike the eardrum in your ear

The higher the frequency of sound, the higher the pitch

The movement of an object toward a subject compresses sound waves (and increases the pitch) whereas movement away from a subject rarefies the sound waves (decreasing the pitch)

When the source of the sound is stationary, the sound wave fronts reach both observes with an equal frequency and therefore equal pitch

When the source of the sound is moving toward a subject, the sound wave fronts are compressed, creating an apparent increase in frequency, and therefore a much higher pitch.

High pitch Low pitch

The Doppler Effect occurs in both mechanical (e.g. sound) and non-mechanical (e.g. EMR) waves.

Trivia: What happens with the situation below?

Wave Interactions

When waves interact with an obstacle, three things can happen:

1. Reflection: the bouncing back of a wave as it meets a surface or boundary

2. Diffraction: the bending of a wave as it passes an edge or an opening

3. Refraction: the bending of a wave as it passes from one medium to another

Reflection

Waves reflect at “free” boundaries See Figure 11-16 A, p 374.

Waves reflect and invert at “fixed” boundaries. See Figure 11-16 B, p 374.

Diffraction

Diffraction is the bending of waves around an obstacle. See Figure 11-17, p 375.

Refraction

Refraction is the bending of waves as they pass from one medium to another (and the wave speed is changed)

No change in wave speed = no refraction

Interference

When different waves occur in the same place, they combine together to produce a single wave…this is called Interference

Waves are always added together in Interference

If the resulting interference wave is greater than either original waves, the result is called “constructive interference”

If the resulting interference wave is smaller than largest original wave, the result is called “destructive interference”

Standing Waves

Standing waves are produced when an original wave and a reflected wave of the same amplitude and frequency interfere with each other.

Standing waves produce what appears to be a wave that does not move and contains regions with no vibrations (i.e. nodes) and maximum vibrations (i.e. antinodes)

See Figure 11-23, p 380