Waves

How to produce a wave in spring?• Give one end of a spring a quick

wiggle/shake at right angles to the spring.

• Flip one end of a spring at right angle to the length of the spring.

• Give a quick wiggle/shake to and fro along the length of spring.

How to make a wave in water?

• Put some pieces of cork on the water and move the cork up and down.

• Touch the surface of the water.

4

Defining a Wave

•Wave: A way in which energy and information may be transferred from place to place without physical movement of material from one location to another.

Types /Categories of Waves

•Waves come in many shapes and forms. While all waves share some basic characteristic properties and behaviors, some waves can be distinguished from others based on some observable (and some non-observable) characteristics. It is common to categorize waves based on these distinguishing characteristics.

Types /Categories of Waves• One way to categorize waves is on the basis

of their ability or inability to transmit energy through a vacuum

• Mechanical waveare any waves that move through a medium.

• Electromagnetic wave are vibrating electric and magnetic fields that progress through space. P160

•Progressive wave: Waves that travel, or propagate, from a source are called progressive waves. 

A progressive wave or travelling wave consists of a vibration carrying energy from a source to the surroundings

•Stationary wave

There are two different types of progressive waves:

Transverse waves –

vibrations/disturbances

are perpendicular to the wave motion

Crest and trough in the waveform.

There are two different types of progressive waves:

Transverse waves –

Longitudinal waves-

One way to categorize waves is on the basis of the direction of movement of the individual particles of the medium relative to the direction that the waves travel.

11

•A transverse wave can be made by vibrating the left hand side of a piece of rope up and down.

•If you could freeze the action you would see the wave has the shape shown below.

•Energy transferred•Energy is transferred along the rope away

from the source of the wave.

Transverse wave character

12•The parts of a transverse wave are given the names:

•Peak

•Trough

Parts of a transverse wave

Longitudinal waves

• vibrations are parallel to the wave motion - so if the wave is travelling horizontally, the particles will be compressed closer together horizontally, or expanded horizontally as they go along (we call the expanded bit a rarefaction).  The particle movement is a series of compressions and rarefactions.  For example, sound and some earthquake waves.

Sound waves are longitudinal

Graphical Representation of Waves

• 横坐标——表示在波的传播方向上各质点的平衡位置于波源的距离。

• X-axis-------The distance for each points on the medium away from the source of the vibration.

• 纵坐标——表示某一时刻各质点偏离平衡位置的位移。

• Y-axis-------The displace of the points away from their equilibrium position.

For T- wave

For L-wave

• The particles either move up and down or from side to side as the wave goes past (like waves on the surface of the sea).After the wave has gone, the particles are back where they started.--------Equilibrium position.

Quantity in waves• Displacement(d): The distance of a point

on the waveform from its undisturbed position/equilibrium position.

• The production and travelling of the wave机械波的形成与图像.swf

• Amplitude(A): The maximum displacement of the medium from its equilibrium position.

• Wavelength(λ): the distance the wave has traveled during one complete cycle

• the distance moved by the disturbance during one time period.

• You can find out the wavelength by the distance between two successive crest (or trough) -------(for transverse wave)

The distance between two successive compressions (or rarefactions) -------longitudinal wave

Quantity in waves

• Period(T): The time for one complete wave to pass a fixed point. (unit: s)

• Period(T): The time for one complete cycles of vibration of a particle(unit: s)

What factor does Period of the wave depend on?

measurement

Quantity in waves

• Frequency(f): The number of waves pass through a fixed point per unit time. (unit: Hz)

• Frequency(f): The number of cycles of vibration of a particle in per unit time. (unit: Hz)

• T=1/f T is the reciprocal of f.

• Speed of wave

fftime

cedisv

/1cycle onefor taken

cycle onein travelledtan

• Speed of electromagnetic wave in the vacuum?

What factor does wave speed depend on?

28

Wave Cycles Time (s) Freq(Hz)

2

2

2

•Complete the table:

29

Wave equation example 1

•What is the velocity of a water wave with a 2 m wavelength, whose frequency is 0.5 Hz?

• Velocity = Frequency Wavelength

• v = f

• v = 0.5 2

• v = 1 m/s.

30

Wave equation example 2

•What is the velocity of green light travelling through a vacuum with a wavelength of 600 nm, if its frequency is 5 1014 Hz?

• Velocity = Frequency Wavelength

• v = f

• v = 5 1014 Hz 600 nm

• v = (5 1014) (600 10-9)

• v = 3 108 m/s.

31

Wave equation example 3

•What is the wavelength of a low frequency sound wave vibrating at 20 Hz if the speed of sound is 330 m/s ?

• Velocity = Frequency Wavelength

• Wavelength = Velocity Frequency

• = 330 m/s 20 Hz

• = 17 m .

32

Wave equation example 4

•What is the speed of a 4000 Hz sound wave travelling through a railway line with a wavelength of 0.75 m ?

• Velocity = Frequency Wavelength

• Velocity = 0.75 m 4000 Hz

• Velocity = 3.0 103 m/s.•Sound waves travel much faster through solid materials as the particles are much closer together than they are in a gas.

Wavefront

• A wavefront is a line or surface on which the disturbance has the same phase at all points.

• Wavefront is perpendicular to the direction of the wave motion.

34

•The photograph shows waves travelling across the surface of a pond.

•The wavelength is estimated at 0.15m.

1m

•If the frequency of the wave is 0.2 Hz, what is the speed of the wave?

•wave speed = frequency x wavelength

•wave speed = 0.2 x 0.15

•wave speed = 0.03 ms-1

Wave equation example 5

Polarisation/ Polarization

• Polarisation is the process by which the oscillations are made to occur in one plane only.

This idea is used in Polaroid glasses to reduce the amount of light able to reach the eye. Polarisation also has to be taken into account when transmitting and receiving waves.

• Polarisation is a phenomenon associated with transverse waves.

• Longitudinal waves cannot be polarised.

Introduction to the Cathode Ray Oscilloscope (CRO)

A schematic diagram of the CRO

Inside a CRO

d.c. supply

a.c. supply

=

a.c.

+

Panel Controls of CRO

Panel Controls of CRO

As you can see, the screen of this oscilloscope has 8 squares or divisions on the vertical axis, and 10 squares or divsions on the horizontal axis. Usually, these squares are 1 cm in each direction:

The DISP / DIV control determines the vertical scale of the graph drawn on the oscilloscope screen.

Y-Gain

The gain control (增益控制 ) (or Y-gain) of the Y-plates is calibrated in V/cm or mV/cm.

A gain of 2 V/cm the spot is deflected 1 cm for every

2 V applied across the Y-plates.

The TIME / DIV control determines the horizontal scale of the graph which appears on the oscilloscope screen.

Time Base

The time base control is calibrated in s/cm, ms/cm or s/cm.

A time base of 5 ms/cm the electron beam

takes 5 ms to sweep 1 cm across the screen

With 10 squares across the screen and the spot moving at 0.2 s / DIV, how long does it take for the spot to cross the screen? Check your answer using a stopclock.

Other useful controls

Calibrating a CRO

Example 3

voltage gain = 2 V/cmtime base = off

1 complete waveform= 4 cm

Time base = 5 ms/cm and an a.c. signal is shown. Find the frequency of the a.c.

period of wave = time for 1 cycle= 4 5= 20 ms = 0.02 s

frequency = 1/period = 1/0.02= 50 Hz

Electro-magnetic Waves

Type of ray:

Gamma rays: X-rays:Ultraviolet

:Visible light:

Production:

Emitted during radioactive decay

Produced by firing electrons at a metal target

Emitted by the Sun

Emitted by the Sun

Uses:Medicine in chemotherapy

Medicine for looking at bones

Tanning Seeing

Hazards:Causes cancer by damaging cells

Causes cancer by damaging cells

Can cause skin cancer

Intense light can damage your sight

Wavelength (m): ×10-12 × 10-10 × 10-8 7 × 10-7 ~ 4

× 10-7

Frequency (Hz): × 10 20 × 10 18 ×10 15 × 10 14

Electro-magnetic Waves

Type of ray: Infra red: Micro-waves: Radio-waves:

Production:Emitted by hot objects

Produced by changing currents in a conductor

Produced by changing currents in a conductor

Uses:Conventional cooking

Microwave cooking and communications

Communication and media

Hazards: Can burn Can burnCurrently not considered to be hazardous

Wavelength (m): × 10-5 × 10-3  to  × 10-2 × 1

Frequency (Hz): ×10 12 × 10 10 ×10 8 to×10 10

All of the waves in the electromagnetic spectrum are oscillating electric and magnetic fields. These fields are perpendicular to each other.

• An aerial has to be aligned to the plane of the polarised waves for it to receive the maximum signal.

Electro-magnetic Waves• All the waves in the electromagnetic

spectrum…

• -travel the same speed in a vacuum; c=3.0×108m/s

• -can be reflected, refracted, diffracted and polarised;

• -are transverse waves.It is important that you are able to rememeber the different parts of the electromagnetic spectrum and their properties.

• If the vibrations of a wave are at right angles to the direction of the wave, it is called a . . . . . . . . . . . . . . . . . wave.

If the vibrations of a wave are along the direction of the wave, it is called a . . . . . . . . . . . . . . . . . . wave.A water wave is a . . . . . . . . . . . . . . . . . wave and a sound wave is a . . . . . . . . . . . . . . . . wave.

• The wavelength of a wave is the . . . . . . . . . . . . . . . . . . between two successive . . . . . . . . . . . . . . . . . (or . . . . . . . . . . . . . . . . . ) The frequency of a vibration is measured in . . . . . . . . . . . . . . . . . . or

• Rarefaction (pronounced rair - ree - fac - shun)is the name given to the region where the coils of the spring are pulled apart.

• Compression is the name given to the region where the coils of the spring are pushed together.

• Sound is caused by . . . . . . . . . . . . . . . . . .

• A sound wave consists of places at higher pressure (called . . . . . . . . . . . . . . .) and places of . . . . . . . . . . . . . . pressure (called . . . . . . . . . . . . . . .. . . . . .. . .)

• Wave speed (in metres per second) equals frequency (in . . . . . . . . . ) multiplied by . . . . . . . . . . . . . . . . . . (in . . . . . . . . . .)

• Sound cannot travel through a . . . . . . . . . . . . . . . . . . .

• Echoes are caused by the . . . . . . . . . . . . . . . . . . . . . of sound.

• The speed of sound in a solid is . . . . . . . . . . . . . . . . . . than the speed of sound in air.

• Ultrasounds have a . . . . . . . . . . . . . . . . . . above . . . . . . . . . . Hz and so have a short . . . . . . . . . . . . . . . . . . .They have many uses, including pre-natal . . . . . . . . . . .

• Pitch depends on . . . . . . . . . . . . . . . . . . Loudness depends on . . . . . . . . . . . . . . . . . . Quality depends on . . . . . . . . . . . . . . . . . .

Sound wave and musical notes

• 1. Pitch depends on the frequency , the higher the frequency the higher the sound the receiver hear.

• 2. Loudness depends on the amplitude. The stronger the object vibrate the bigger the loudness.

• 3. The Quality of the instrument depends on the numbers of fundamental and overtones.