You are on page 1of 19

# 1

WAVES
Types of Waves
Pulses
Pulses are disturbances or a single wave motion. A continuous production of pulses will
give rise to a progressive wave (wave train).

Progressive Waves
A progressive wave is the movement of a disturbance which carries energy away from a
source.

Stationary Waves
A stationary wave is a disturbance which does not travel and is produced by the
simultaneous traveling of two identical waves in opposite directions. Net energy is not
taken to nor delivered to the source.

## There are two types of waves:

i.
Transverse Waves
ii. Longitudinal Waves

D. Whitehall

2
Transverse Waves
If you hold a slinky, while having the other end fixed, and waggled it from side to side,
you will see that coils of the slinky move in the same way as your hand movement.
The wave moves in one direction while the oscillations of the slinky move at right angles
to it.

A transverse wave is one which the displacement of the particles is at right angles to
direction the wave is traveling.

Longitudinal Waves
If you push and pull one end of a slinky (while the other end is fixed) you will notice that
the parts of the slinky move forward and backwards in the same direction the wave is
moving.

## A longitudinal wave is one in which the displacement of the particles is in line or

parallel to the direction in which the wave is moving.

D. Whitehall

3
Ripple Tank

We can also use a ripple tank to observe waves. If we set up the ripple tank as shown in
the diagram (and dip a pencil into the water without touching the bottom or shaking the
tank), we will see that pulses create waves which have circular wave fronts.

If we take a straight bar and dip it in and out of the ripple tank quickly, the waves that are
produced are called plane surface waves.

D. Whitehall

Wave Parameters
Speed (c / v)
Units: m/s
The speed is the distance moved forward by the crest/ trough (compression / rarefaction)
in one second. This is the speed of propagation or travel of the wave.

## speed = frequency * wavelength

c = f*d
v = f*

Frequency (f)
Units: Hertz (Hz)
The frequency is the number of waves passing any given point in one second or the
number of complete vibrations made in one second.

frequency = ___1___
period

Wavelength ()
Units: metre
The wavelength is the distance between two adjacent or successive crests/ troughs/
compressions/ rarefactions. Therefore, the wavelength is the distance between two
successive particles which are exactly at the same point in their points at the same time
and moving in the same direction.

Period (T)
Units: seconds
The period is the time taken for a particle to complete one oscillation.

period

= ___1___
frequency

Amplitude
The amplitude is the height of the crest or the depth of a trough measured from the
undisturbed position (i.e. It is the maximum displacement of a particle from the rest
position)
Phase
The phase is a measure of timing relationship between two waves or two different points
on one wave.

D. Whitehall

Graphs
We can use two types of graph to represent a wave:
(A)

## A displacement - position graph is like a photograph of a transverse wave at a given

instant in time. It gives the information about the displacements at different positions
along the wave at a given instant.
It is not possible to determine if the wave is a transverse or longitudinal by looking at the
graph. It is not possible to extract time related information from this graph.

(B)

## Displacement Time Graph

The displacement time graph applies to the vibration of an arbitrarily chosen single
particle in a wave. It is not possible to determine if the wave is transverse or longitudinal
and it is not possible to deduce the wavelength or the speed from this graph.
D. Whitehall

Summary

an instant

## Represent the motion of ONE wave

particle over a period of time

Can obtain:
Amplitude
Wavelength

Can obtain:
Amplitude
Period

information

## Cannot determine wavelength or

speed related information.

## Cannot determine if the wave is a

transverse or longitudinal wave

## Cannot determine if the wave is a

transverse or longitudinal wave

D. Whitehall

Properties of Waves
All waves have the same properties of
i.
Reflection
ii. Refraction
iii. Diffraction

Reflection
We can use water waves to observe their behaviour. Observation of the water waves
show that when they reach a barrier or the boundary of the water, they are sent backwards
(reflected). The properties of water waves are similar to those of light rays and the effect
is similar to that of light rays reflecting in a mirror.

The laws which govern the reflection of light also apply to the reflection of waves,
provided that we can properly relate the wave diagrams to the equivalent ray diagrams.
Laws of Reflection:
i.
The angle of incidence and the angle of reflection are equal
ii. The incident ray, the reflected ray and the normal all lie in the same plane

D. Whitehall

8
Refraction
Water waves refract as they move from one depth of water to another. Refraction occurs
because the wave changes speed as it crosses the boundary.

We can observe this change when surface water waves are at a boundary between deep
and shallow water.
This phenomenon relates the change of direction to the change of speed as the wave
travels from deep to shallow water.

The frequency of the wave remains unchanged during refraction but the velocity and
the wavelength changes.

We can find the refractive index of the wave by using Snells Law

sin i =
sin r

v1 =
v2

1
2

D. Whitehall

9
Diffraction
Waves bend around gaps and edges of obstacles. This bending is called diffraction. Plane
waves can generate circular waves when diffraction occurs.

When the wavelength is small compared to the gap we can see diffraction at each edge.

When the gap is small compared to the wavelength we obtain circular waves.

We can obtain greater diffraction either by decrease the size of the gap or increasing the
wavelength of the incident wave.
There is no change in frequency or wavelength results from diffraction.

D. Whitehall

10
Interference
When two waves of the same kind meet each other (superpose), their individual effects
combine and a resulting effect is produced. The net displacement is the sum of the
original displacements of the two waves.
We can demonstrate this type of interference by using a monochromatic source of light
and double slit as shown in the diagram below.

The emerging wavetrains of light will have the same frequency and a constant phase
relationship with each other. The two illuminated slits are called COHERENT
SOURCES of light.

D. Whitehall

11
We can also demonstrate interference by using the ripple tank. The same effect can be
obtained by using plane waves that are incident to two small gaps. Circular waves are
formed at gaps and interference occurs as a result of the circular wave overlapping.
If the slit spacing increases then the lines of interference becomes close together.
However, if the wavelength of the wave increases then the lines of interference moves
further apart.

Constructive Interference
When two waves meet in phase, i.e. the crest of one wave falls on the crest of another
wave (or trough of one wave falls on the trough of another wave), the result is a large
displacement.

Destructive Interference
When two waves meet out of phase, i.e. the crest of one wave falls on the trough of
another wave), the result is cancellation.

D. Whitehall

12

SOUND WAVES
Production and Propagation
Sound is produced by vibrating systems. The table below gives examples of musical
instruments and the vibrating systems linked to them.

The vibrating systems affect the particles of the medium in which they vibrate. Sound is
propagated as a longitudinal wave and sound energy moves in a set of compressions and
refractions.

We can demonstrate that sound does not travel in a vacuum by using one of the apparatus
below.

Before the vacuum pump is turned on, air is in the pump and the bell is heard. However,
when the air is pumped out, no sound is heard even though the hammer is hitting the
gong. This demonstrates that sound cannot be transmitted in a vacuum: a material
medium is necessary.

D. Whitehall

13
Speed
The speed of sound in air is approximately 330 m/s at a temperature of 0oC but varies
depending on the temperature.
We can estimate the speed of sound in air. First find a large wall or building which will
be used as a reflector for sound. Then stand a known distance, about 100 m, from the wall
and clap hands together and listen for an echo. Repeat the clapping until the echo is heard
clearly.
Increase the clapping until each clap coincides with the echo heard. Measure the time for
50 claps and divide by 50 to find the time taken for one clap. This is the time for the
sound to travel to the wall and return as the echo.
We can calculate the speed of sound by using the equation:
speed = 2 * distance between the wall and the source
time interval between echoes

Audio Frequencies
Sound can be produced with different frequency and can be classified as a pure note, a
musical note or noise. When notes are composed with a single frequency they are usually
pleasing to the ear.
Musical notes consist of waves having fundamental frequencies and other frequencies
called overtones. These overtones are produced when the vibrations take place in a
different manner from that of the fundamental.
Noise is sound which made up of a mixture of frequencies which are not overtones and
maybe unpleasant to the ear.
Musical notes have three main properties:
The Pitch
The pitch of a note is its position in the musical scale. It measures how high or low the
note sounds. As the frequency increases the pitch also increases.
Loudness
Loudness is the magnitude of the sensation produced when a sound reaches the ear. The
larger the amplitude of the vibrations reaching the ear, the louder the sound is heard.
Quality
The quality distinguishes between musical notes of the same frequency played on
different instruments. The way an instrument sounds is called its quality or tone.

D. Whitehall

14
Reflection
We can demonstrate that sound waves can be reflected, by using apparatus shown in the
diagram below.

A cardboard tube is mounted using a retort stand and directed towards a hard smooth
wall. A mark was made where the sound beam is expected to strike and another tube was
placed where the reflected tube would be. The tube was adjusted until a position was
found where the reflected sound was the loudest.
From this experiment we can determine that the angle of incidence is equal to the angle
of reflection and that sound obeys the law of reflection.
Hard smooth surfaces reflect sound. However, soft surfaces such as curtains and carpets
are good absorber of sound. Reflected sound is called an echo and plays an important role
in allowing us to hear sounds.

D. Whitehall

15

Refraction
We can demonstrate that sound waves can be refracted, by using apparatus shown in the
diagram below.

## A loudspeaker is connected to a signal generator and hung in a retort stand. A

microphone is connected to an electronic voltmeter directly below the loudspeaker. The
signal generator is turned on and level of sound picked up by the microphone on the
electronic voltmeter is noted.
A balloon filled with carbon dioxide is placed between the loudspeaker and the
microphone and the level of sound picked up by the microphone is noted.
The balloon acts as a lens since sound travels more slowly in carbon dioxide than in air at
the same temperature and pressure. Thus the sound is refracted and focused and this
explains why the level of sound increases when the balloon is placed in the space.

Diffraction
Sounds of high frequency have waves of small wavelengths and sounds of low frequency
have waves of great wavelengths. Diffraction of sound occurs when the gap is the same
size compared to that of the wavelength of the sound. If the gap is just wider than the
wavelength the sound spreads and allows us to hear around corners. If the gap is much
larger than the wavelength, it does not spread as much and the diffraction is limited.

D. Whitehall

16

ELECTROMAGNETIC WAVES

D. Whitehall

17

D. Whitehall

18

D. Whitehall

19

PFC

## Page 411 - 423

vibrations in a vacuum
reflection of sound
refraction of sound waves
beats
music and noise
direction and measuring sound
human ear
the problem of noise

## Page 435 - 439

electromagnetic family
above visible light
below visible light
The provided text is an educational passage that covers various aspects of waves, including types of waves, wave parameters, properties of waves, sound waves, and electromagnetic waves. It does not contain any specific mathematical questions or answers to such questions.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
You are on page 1of 19

# 1

WAVES
Types of Waves
Pulses
Pulses are disturbances or a single wave motion. A continuous production of pulses will
give rise to a progressive wave (wave train).

Progressive Waves
A progressive wave is the movement of a disturbance which carries energy away from a
source.

Stationary Waves
A stationary wave is a disturbance which does not travel and is produced by the
simultaneous traveling of two identical waves in opposite directions. Net energy is not
taken to nor delivered to the source.

## There are two types of waves:

i.
Transverse Waves
ii. Longitudinal Waves

D. Whitehall

2
Transverse Waves
If you hold a slinky, while having the other end fixed, and waggled it from side to side,
you will see that coils of the slinky move in the same way as your hand movement.
The wave moves in one direction while the oscillations of the slinky move at right angles
to it.

A transverse wave is one which the displacement of the particles is at right angles to
direction the wave is traveling.

Longitudinal Waves
If you push and pull one end of a slinky (while the other end is fixed) you will notice that
the parts of the slinky move forward and backwards in the same direction the wave is
moving.

## A longitudinal wave is one in which the displacement of the particles is in line or

parallel to the direction in which the wave is moving.

D. Whitehall

3
Ripple Tank

We can also use a ripple tank to observe waves. If we set up the ripple tank as shown in
the diagram (and dip a pencil into the water without touching the bottom or shaking the
tank), we will see that pulses create waves which have circular wave fronts.

If we take a straight bar and dip it in and out of the ripple tank quickly, the waves that are
produced are called plane surface waves.

D. Whitehall

Wave Parameters
Speed (c / v)
Units: m/s
The speed is the distance moved forward by the crest/ trough (compression / rarefaction)
in one second. This is the speed of propagation or travel of the wave.

## speed = frequency * wavelength

c = f*d
v = f*

Frequency (f)
Units: Hertz (Hz)
The frequency is the number of waves passing any given point in one second or the
number of complete vibrations made in one second.

frequency = ___1___
period

Wavelength ()
Units: metre
The wavelength is the distance between two adjacent or successive crests/ troughs/
compressions/ rarefactions. Therefore, the wavelength is the distance between two
successive particles which are exactly at the same point in their points at the same time
and moving in the same direction.

Period (T)
Units: seconds
The period is the time taken for a particle to complete one oscillation.

period

= ___1___
frequency

Amplitude
The amplitude is the height of the crest or the depth of a trough measured from the
undisturbed position (i.e. It is the maximum displacement of a particle from the rest
position)
Phase
The phase is a measure of timing relationship between two waves or two different points
on one wave.

D. Whitehall

Graphs
We can use two types of graph to represent a wave:
(A)

## A displacement - position graph is like a photograph of a transverse wave at a given

instant in time. It gives the information about the displacements at different positions
along the wave at a given instant.
It is not possible to determine if the wave is a transverse or longitudinal by looking at the
graph. It is not possible to extract time related information from this graph.

(B)

## Displacement Time Graph

The displacement time graph applies to the vibration of an arbitrarily chosen single
particle in a wave. It is not possible to determine if the wave is transverse or longitudinal
and it is not possible to deduce the wavelength or the speed from this graph.
D. Whitehall

Summary

an instant

## Represent the motion of ONE wave

particle over a period of time

Can obtain:
Amplitude
Wavelength

Can obtain:
Amplitude
Period

information

## Cannot determine wavelength or

speed related information.

## Cannot determine if the wave is a

transverse or longitudinal wave

## Cannot determine if the wave is a

transverse or longitudinal wave

D. Whitehall

Properties of Waves
All waves have the same properties of
i.
Reflection
ii. Refraction
iii. Diffraction

Reflection
We can use water waves to observe their behaviour. Observation of the water waves
show that when they reach a barrier or the boundary of the water, they are sent backwards
(reflected). The properties of water waves are similar to those of light rays and the effect
is similar to that of light rays reflecting in a mirror.

The laws which govern the reflection of light also apply to the reflection of waves,
provided that we can properly relate the wave diagrams to the equivalent ray diagrams.
Laws of Reflection:
i.
The angle of incidence and the angle of reflection are equal
ii. The incident ray, the reflected ray and the normal all lie in the same plane

D. Whitehall

8
Refraction
Water waves refract as they move from one depth of water to another. Refraction occurs
because the wave changes speed as it crosses the boundary.

We can observe this change when surface water waves are at a boundary between deep
and shallow water.
This phenomenon relates the change of direction to the change of speed as the wave
travels from deep to shallow water.

The frequency of the wave remains unchanged during refraction but the velocity and
the wavelength changes.

We can find the refractive index of the wave by using Snells Law

sin i =
sin r

v1 =
v2

1
2

D. Whitehall

9
Diffraction
Waves bend around gaps and edges of obstacles. This bending is called diffraction. Plane
waves can generate circular waves when diffraction occurs.

When the wavelength is small compared to the gap we can see diffraction at each edge.

When the gap is small compared to the wavelength we obtain circular waves.

We can obtain greater diffraction either by decrease the size of the gap or increasing the
wavelength of the incident wave.
There is no change in frequency or wavelength results from diffraction.

D. Whitehall

10
Interference
When two waves of the same kind meet each other (superpose), their individual effects
combine and a resulting effect is produced. The net displacement is the sum of the
original displacements of the two waves.
We can demonstrate this type of interference by using a monochromatic source of light
and double slit as shown in the diagram below.

The emerging wavetrains of light will have the same frequency and a constant phase
relationship with each other. The two illuminated slits are called COHERENT
SOURCES of light.

D. Whitehall

11
We can also demonstrate interference by using the ripple tank. The same effect can be
obtained by using plane waves that are incident to two small gaps. Circular waves are
formed at gaps and interference occurs as a result of the circular wave overlapping.
If the slit spacing increases then the lines of interference becomes close together.
However, if the wavelength of the wave increases then the lines of interference moves
further apart.

Constructive Interference
When two waves meet in phase, i.e. the crest of one wave falls on the crest of another
wave (or trough of one wave falls on the trough of another wave), the result is a large
displacement.

Destructive Interference
When two waves meet out of phase, i.e. the crest of one wave falls on the trough of
another wave), the result is cancellation.

D. Whitehall

12

SOUND WAVES
Production and Propagation
Sound is produced by vibrating systems. The table below gives examples of musical
instruments and the vibrating systems linked to them.

The vibrating systems affect the particles of the medium in which they vibrate. Sound is
propagated as a longitudinal wave and sound energy moves in a set of compressions and
refractions.

We can demonstrate that sound does not travel in a vacuum by using one of the apparatus
below.

Before the vacuum pump is turned on, air is in the pump and the bell is heard. However,
when the air is pumped out, no sound is heard even though the hammer is hitting the
gong. This demonstrates that sound cannot be transmitted in a vacuum: a material
medium is necessary.

D. Whitehall

13
Speed
The speed of sound in air is approximately 330 m/s at a temperature of 0oC but varies
depending on the temperature.
We can estimate the speed of sound in air. First find a large wall or building which will
be used as a reflector for sound. Then stand a known distance, about 100 m, from the wall
and clap hands together and listen for an echo. Repeat the clapping until the echo is heard
clearly.
Increase the clapping until each clap coincides with the echo heard. Measure the time for
50 claps and divide by 50 to find the time taken for one clap. This is the time for the
sound to travel to the wall and return as the echo.
We can calculate the speed of sound by using the equation:
speed = 2 * distance between the wall and the source
time interval between echoes

Audio Frequencies
Sound can be produced with different frequency and can be classified as a pure note, a
musical note or noise. When notes are composed with a single frequency they are usually
pleasing to the ear.
Musical notes consist of waves having fundamental frequencies and other frequencies
called overtones. These overtones are produced when the vibrations take place in a
different manner from that of the fundamental.
Noise is sound which made up of a mixture of frequencies which are not overtones and
maybe unpleasant to the ear.
Musical notes have three main properties:
The Pitch
The pitch of a note is its position in the musical scale. It measures how high or low the
note sounds. As the frequency increases the pitch also increases.
Loudness
Loudness is the magnitude of the sensation produced when a sound reaches the ear. The
larger the amplitude of the vibrations reaching the ear, the louder the sound is heard.
Quality
The quality distinguishes between musical notes of the same frequency played on
different instruments. The way an instrument sounds is called its quality or tone.

D. Whitehall

14
Reflection
We can demonstrate that sound waves can be reflected, by using apparatus shown in the
diagram below.

A cardboard tube is mounted using a retort stand and directed towards a hard smooth
wall. A mark was made where the sound beam is expected to strike and another tube was
placed where the reflected tube would be. The tube was adjusted until a position was
found where the reflected sound was the loudest.
From this experiment we can determine that the angle of incidence is equal to the angle
of reflection and that sound obeys the law of reflection.
Hard smooth surfaces reflect sound. However, soft surfaces such as curtains and carpets
are good absorber of sound. Reflected sound is called an echo and plays an important role
in allowing us to hear sounds.

D. Whitehall

15

Refraction
We can demonstrate that sound waves can be refracted, by using apparatus shown in the
diagram below.

## A loudspeaker is connected to a signal generator and hung in a retort stand. A

microphone is connected to an electronic voltmeter directly below the loudspeaker. The
signal generator is turned on and level of sound picked up by the microphone on the
electronic voltmeter is noted.
A balloon filled with carbon dioxide is placed between the loudspeaker and the
microphone and the level of sound picked up by the microphone is noted.
The balloon acts as a lens since sound travels more slowly in carbon dioxide than in air at
the same temperature and pressure. Thus the sound is refracted and focused and this
explains why the level of sound increases when the balloon is placed in the space.

Diffraction
Sounds of high frequency have waves of small wavelengths and sounds of low frequency
have waves of great wavelengths. Diffraction of sound occurs when the gap is the same
size compared to that of the wavelength of the sound. If the gap is just wider than the
wavelength the sound spreads and allows us to hear around corners. If the gap is much
larger than the wavelength, it does not spread as much and the diffraction is limited.

D. Whitehall

16

ELECTROMAGNETIC WAVES

D. Whitehall

17

D. Whitehall

18

D. Whitehall

19

PFC

## Page 411 - 423

vibrations in a vacuum
reflection of sound
refraction of sound waves
beats
music and noise
direction and measuring sound
human ear
the problem of noise

## Page 435 - 439

electromagnetic family
above visible light
below visible light
user
The provided text is an educational passage that covers various aspects of waves, including types of waves, wave parameters, properties of waves, sound waves, and electromagnetic waves. It does not contain any specific mathematical questions or answers to such questions.

TYPE: NO_QUESTION