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### Waves

posted Feb 1, 2015, 11:58 PM by ranmini@charliesresearch.com   [ updated Jun 25, 2018, 9:19 PM by Upali Salpadoru ]

Fig.1 Ribbon dancers waving ribbons.

Fig.2 Maz riding the waves.

"Maz Quinn is possibly the best-known New Zealand surfer"
He rides the waves as fast as he rides a racing cycle.

How are these produced?

Where else do the waves exist?

Nelly’s father,  waves to her and her mom as he goes to office. The red flags are waving
(fluttering) due to the wind What exactly is a wave?

Fig.3 Waving and waves.

Let us start with the waving of the hand. You move your hand this way and that way; a ‘to & fro’ movement. This kind of rhythmic   movements are called ‘vibrations’.

So can this motion produce a ‘wave’?

Yes it can!”, exclaimed Nelly, waving a ribbon.

You also can get hold of a ribbon and wave
it in different ways to observe the patterns you get.  If you think you can't figure it, take
a pencil and a long paper.  Keep the pencil to the paper and ask a friend to pull the
paper. What will you get ? A straight line.

Next time keep your hand moving to & fro when the paper is pulled ?

What do you get? It will be similar to the diagram below.

This is what we call a wave pattern.

An upward curve, called a crest, alternates with a downward curve , called a trough.

A crest and a trough form one cycle.

Fig.4  Wave form.

In the ribbon demonstration, as the ribbon is moving you cannot observe the motion of a wave. Ali has a wonderful experiment to show how the waves travel. He takes a rope and ties one end to a tree. Then he pulls the rope at the other end and waves rapidly. This is a very good experiment to understand the waves.  Ali moves the hand up and down; the wave travels to the tree. The rope does not move towards the tree.

These experiments show us that when matter vibrates, waves propagate.(spread). In liquids such as water, or in solids such as a table or the Earth waves can spared in all directions.

Fig.5  The horizontal spreading ripples are produced by vertical vibration of water molecules.

Experiment  1.

Aim:- To determine the Speed of a waves

Nelly  used a garden hose for this experiment.  When ever she jerked her hand upwards , a crest, half a wave traveled to the tap end.

If you measure the distance and the time it will take a disturbance to travel along the hose you can calculate the speed of the wave.

Fig.6  Measuring the speed of a wave.

Calculation
Length  the wave travels    =    ……….. m
The time taken                  =   ………...s

Therefore speed                = …………m /  ………….s

The distance divided by time will give the speed of the wave.
Your investigations need not stop here. You can try different hose pipes and ropes.  Those who are eager for research  can investigate the following;

Experiment  2.

Take a marker pen placing it on paper and move the hand up and down. What will you get ?  You will get a vertical line. On the same line you will be drawing again and again.  Now get a friend to pull the paper to a side while you are drawing. What will you get ?

Fig.7 This is what we got.

Let us learn the parts and the working of a wave.
The  ‘too and fro movement’ of the marker  is called oscillations or vibrations. When the marker goes up from the resting position, comes back and goes deep down and gets back, it completes one cycle. By this time a crest and a trough will form.
The number of such cycles form during one second is called frequency. The unit for this is Hertz, (Hz), The wave length is the distance the wave travels for  one complete cycle.  The furthest displacement of the marker from the resting position is the amplitude

 Term Definition Term Definition Amplitude The maximum displacement from the mid line Crest The upward curve Trough The downward curve Cycle One crest and one trough Wave length The distance wave travels  for one cycle. Frequency The number of cycles in one second.
 Activity  (for brainy children)If you are clever you will be able to work out a connection between the speed of the wave, wavelength and the frequency

What is a wave?  ........It is a A method by which energy is transferred

One way to differentiate waves is to consider the medium in which they travel. The waves we consider so far travel either in solids or liquids.

 Are there waves that travel in air and ? "Yes !  Sound, light, TV and radio waves." Can the sound waves travel in space? No. Light and radio waves can travel in space.

Waves may be classified as follows:-

 Mechanical waves’ Electromagnetic waves. 1.Uses molecules for propagation.2.Unable to travel in a vacuum or in space.3.Speeds vary widely. 4. There are two modes of travel called Transverse and Longitudinal. Uses electric and magnetic forces for transmission.Travels even in space.All waves travel at the speed of 3.00 x 108 ms-1 in space.All are transverse waves.

Normally a wave diagram is a graphical representation of shifting of particles in a wave.

Displacement plotted against time.

The  Electromagnetic spectrum.

i..According to the modern theories, there cannot be anything moving faster than these waves. Their speed in space is 300,000,000 meters per second (3.00 x 108).
ii. They are caused by fluctuation of an electric field perpendicular to a magnetic field and perpendicular to the direction of travel. These really are transverse waves.

 Type Frequency Wavelength Remarks / Uses. Radio Waves <3x1011Hz >1mm Communication. Micro waves 3x1011- 1013Hz 1mm - 25um Micro wave ovens. Infra red (heat waves) 1x1013 - 4x1014Hz 25um - 750nm TV remote control uses  a wavelength around 940 nanometers.Heat lamps  emit both visible and infrared energy at wavelengths between 500nm to 3000nm . Light. 4x1014 - 7.5x1014 Hz 750nm - 400 nm7.5x10-7 - 4x10-7 Food production by plants.Photosynthesis. Ultra violet 1015 - 1017 Hz 400nm - 1nm Converts fat layer in skin to vitamin D. Sterilizing food. X' rays. 1017 - 1020Hz 1nm - 1pm Used in medicine. Gamma rays 1020 - 1024 Hz 10-12 m Treatment of cancer.

Fig.4.Light consists of transverse waves . Fluctuating of  electric and magnetic fields.

2.0  Mechanical waves.

These waves can travel only in a material medium. There are three kinds of  such waves.
i.    Longitudinal waves. Ii.    Transverse waves      iii.       Surface waves.

i.    Longitudinal waves:
These can travel in solids, liquids or gases. Particle show only to and fro movement parallel to the direction of travel. Energy is transferred with the wave.
Sound is a very good example of this.

Fig. 5  Spreading of a pressure wave.

The Fig 5 shows how a sound wave is spreading all around in the form of spheres. A vibrating object such as a drum skin or a loud speaker cone will cause very slight changes in air pressure. When the pressure increases we call it a ‘compression’. (Sound waves are often compared to ripples in water which is not correct. They are surface waves)   When the pressure decreases it would be a‘rarefaction’. Air molecules are denoted by curved  lines here.
It is important to note that sound can travel, even in solids and liquids only as longitudinal waves.
A sound wave has a speed of 340ms-1 in air   under normal conditions. 1,484 m/s in water and 0ver 5000 m/s rigid solids.

Fig. 6. A very thin strip of a pressure wave in air. .

A vertical  line stands for a row of molecules in  air.   As the cone of the speaker gets pushed out a compression results. The first compression is labelled as  C 1.  The rows below indicate how it travels to the right.
This can be converted to the wave form by drawing a graph.  The graph  below shows how a single molecule moves . The displacement is given by x axis while time is kept by y axis.

2. Transverse waves.

Take a garden hose or a flexible current  cable. Lay it in the ground. Just give a jerk by lifting the end quickly. You will see a traveling wave pulse. It would be only a crest traveling. Now you can hold the end firmly and swing it to and fro in a horizontal plane.  You will see complete waves traveling. These are transverse waves.
This type of a wave is possible only in solids. The particles vibrate perpendicular to the direction of the wave.

The fig.7. shows a wave traveling to right.

Note that the particles move only in a vertical plane. What can you say about the motion of the particles marked a, b, c, d and e?
a.    Stopped movement, about to turn direction. Maximum gravitational potential energy.
b.    This has the maximum kinetic energy. Velocity up.
c.    This is similar to a but trying to go up. Maximum elastic energy.
d.    This also has the maximum kinetic energy moving down.

Velocity,Wave length and Frequency,

If you understand the definitions o the three wave properties, the connexion between them should be clear.

 Velocity = Wave length x Frequency           V = f. λ

Wave properties.

##### Reflection

To study reflection we must start with linear wave fronts. These can be made by dipping a wooden edge as shown here.

.

Diffraction.

##### Fig. 6.  Pictures  of diffraction.

Diffraction is the bending of waves at the edges or gaps. When a wave passes an edge the corners of the wave front bends. If the gap is smaller than the wave length , the bending at the two edges become noticeable and the resulting fronts progress as curves.

If the gap is large the bending appears only at the edges and is hardly noticeable.

Q.1.0

Give technical terms for these :-
1.The maximum displacement of a particle from the normal position.
2.the distance the wave will go during one complete oscillation
3.The distance between the two nearest particles at the same state of motion.
4.The number of oscillations in one second.
5.The  product of frequency and wave length give?.
4 x 5 = 20 marks

Q.2.0

The two waves have traveled for 0.1  seconds towards right.

1.
 Name Blue wave Red Wave Wave length Period Frequency Velocity
3 x 8=24 marks
2.     Name the particles  that .................

 Category Blue wave Red wave 1.are moving up. 2.Having maximum potential energy. 3  Having maximum kinetic energy. 4. Having zero veleocity.
3 x 8=24 marks

Q.3.0

Q.3.0

Using arrows show the directions the waves will proceed in confronting obstacles.

a. An obstacle b. A shallow region.

6 marks
6 + 6=12  marks.
5x4=20 marks

Q.4.0

The figure shows a sea wave coming ashore. If the shore line is perpendicular to the wavefront explain what changes may occur to the following.

4.1 Direction. 4.2 Wave length 4.3 Velocity 4.4 Frequency 4.5 Amplitude.