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6.1 Vibration And Wave

Posted on 05/02/2010 by amimo5095

Introduction

A wave is produced by a source of vibration.

Mechanical waves need a material medium or their propagation.

Examples of mechanical waves include water waves ,sound waves, shock waves as in earthquakes

and waves in strings, springs and rods.

Electromagnetic waves do not need a material medium for their propagation.

Examples of electromagnetic waves are radio waves , light waves , infra-red (IR) and ultra-violet (

UV).

As a wave travels through a medium, there is no transfer of matter but only transfer of energy from

a vibrating source.

Common terminology of vibrations

Vibration:

A periodic motion where the system performs a repeated to-and-fro motion about an equilibrium

position.

Equilibrium position:

The position of the object where is no resultant force acts on the object.

One oscillation:

To-and-fro motion from the equilibrium position.

Amplitude :

The maximum displacement of the objects from their equilibrium position.

Period, T

The time taken for one complete oscillation.
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The S.I. unit is second (s)

t = time

n = number of oscillations

Frequency, f

The number of complete oscillations per second.

The S.I. unit is Hertz (Hz)

Or

Graph displacement-time

Example 1

A pendulum makes 20 complete oscillations in 24.0 s.

Calculate

(a) the period

(b) the frequency

Solution

Example 2
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Based on he graph above, determine the

(a) amplitude

(b) period

(c) frequency

Solution

Natural Frequency:

The frequency of the free oscillation of a system without any external forces are exerted to the

system.

Factors affecting the natural frequency of the vibration systems.

Vibration system Factors affecting Formula

Oscillation of a

pendulum

length

graviti

Oscillation of a

spring hang with a

mass

Spring constant

mass

Oscillation of a

igsaw blade fixed

with plasticine ball

igsaw contant

mass

Transformation of energy in a vibration system.
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What is meant by Resonance?

A phenomenon that occurs when the frequency of forced vibrations on an object matches the

objects natural frequency and a dramatic increase in amplitude results.

Experiment to show a phenomenon of resonance

The pendulum B ( driver pendulum) is pulled well aside an released so that it oscillates in plane

perpendicular.

All the pendulums oscillate but with different amplitudes.

The pendulum D whose length equals that of the driver (pendulum B) has the greatest amplitude

because its natural frequency of oscillation is the same as the frequency of the driving pendulum.

Examples of Resonance in Everyday Life

Example 1:
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A car or a washing machine may vibrate quite violently at particular speeds. In each case ,resonance

occurs when the frequency of a rotating part ( motor, wheel, drum etc.) is equal to a natural

frequency of vibration of the body of the machine. Resonance can build up a vibration to a large

amplitude.

Example 2:

The story is told of an opera singer who could shatter a glass by singing a note at its natural

frequency.

Example 3:
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The wind ,blowing in gusts, once caused a suspension bridge to sway with increasing amplitude until

it reached a point where the structure was over-stressed and the bridge collapsed.

Example 4:

Wind instruments such as flute, clarinet, trumpet etc. depend on the idea of resonance. Longitudinal

pressure waves can be set up in the air inside the instrument. The column of air has its own natural

frequencies at which it can vibrate. When we blow, we use the mouthpiece to start some vibrations.

Those which happen to match exactly the natural frequencies of the instrument are picked out and

magnified.

Example 5 :

The another example of useful resonance is the tuning circuit on a radio set. Radio waves of all

frequencies strike the aerial and only the one which is required must be picked out. This is done by

having a capacitance-inductance combination which resonates to the frequency of the required

wave . The capacitance is variable; by altering its value other frequencies can be obtained.
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Example 6 :

Microwave ovens use resonance. The frequency of microwaves almost equals the natural frequency

of vibration of a water molecule. This makes the water molecules in food resonate . This means they

take in energy from the microwaves and so they get hotter. This heat conducts and cooks the food.

Example 7 :

The picture showing the insides of the body was produced using magnetic resonance imaging (MRI).

Our bodies contain a lot of hydrogen , mostly in water. The proton in a hydrogen spins . A spinning

charged particle has a magnetic field, so the protons act like small magnets. These are normally

aligned in random directions. Placing a patient in a strong magnetic fields keeps these mini magnets

almost in line. Their field axis just rotates , a bite like a spinning top. This is called processing.

Damping

Damping is a word used to describe how movement and vibrations are reduced or slowed down.

Damping is a process whereby oscillations die down due to a loss of energy to friction forces.

When a system is damped , the amplitude of the of oscillation decreases slowly until the system

stops oscillating.

Damping is usually caused by external frictional forces such as air resistance . It can also be caused

by internal forces , where energy is lost from the system in form of heat.
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In daily use ,e.g. shock absorbers in cars cause oscillations to die down after a car has gone over a

bump in the road.

For another example, damping is introduced intentionally in measurement instruments such as

galvanometer , spring balance etc. to overcome the problem of taking a reading from an oscillating

needle.

6.2 Understanding Wave


Introduction

Oscillations can produce waves. Waves transfer energy from one place to another without

permanently displacing the medium through which they travel.

When we drop a stone into a pond, the kinetic energy of the stone makes the water surface move

up and down near where the stone lands; ripples spread out outwards and if an floating object on

the water some distance away will start to bob up and down. It is becaused the original energy of

the moving stone has been transferred to the object by the wave motion on the water surface.
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When we are at the seaside, we can see large as well as small waves reaching the shore. These

waves arise because of the strong winds in the middle of the sea.The energy of the winds is carried

by the waves to the shore. The water from the middle of the sea does not reach the shore.

The wave motion is regular and repetitive (i.e. periodic motion)

There are two main types mechanical waves such as sound waves and electromagnetic waves.

Transverse waves

Waves in which the direction of vibration of the partticles is perpendicular to the direction of wave

propagation called a transverse wave.

The examples of transerve waves are water waves and electromagnetic waves (radio waves

,microwaves , infra-red (IR) light waves , ultra-violet ( UV), X-rays and gamma rays )

Longitudinal waves

Waves in which the direction of vibration of the particles is parallel to the direction of wave

propagation called a longitudinal wave.

An example of transerve waves is sound waves..

Wave terminology

Amplitude:

The maximum displacement of the medium particles from the equilibrium position.

Period , T:
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The time for one complete oscillations of each particle in the wave.

Frequency, f :

The number of oscillations of each particle in the wave in one second.

Wavelength ,

The distance between two consecutive points which are vibrating in phase.

Or

The distance from one wave crest to the next.

Or

The distance from one wave trough to the next.

Or

Wavespeed , v

The distance moved by a wave in one second.

The wavespeed depends only the medium the waves are traveling through.

Wavefront

The locus of points which vibrates in phase.
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For water waves there are two types of wavefront i.e circular wavefront and plane wavefront.

circular wavefront

plane wavefront

Crest

The point where a wave causes maximum positive displacement of the medium.

Trough

The point where a wave causes maximum negative displacement of the medium

Compression

Region along a longitudinal wave where the pressure and density of particles are higher than when

no wave is passing.

Rarefaction

Region along a longitudinal wave where the pressure and density of particles are lower than when

no wave is passing

The wave equation
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Analysis from the formula

Example 1

A student moves the end of a long spring from side to side 4 times persecond. The wavelength of the

wave on the spring is 0.6 m. With what speed do the waves moves along the spring?

Solution

Example 2

Radio waves travel at a speed 3 x 108

ms-1

. What is the wavelength of FM radio waves received at

200 MHz on your radio dial?

Solution

Example 3

A long rope is stretched out on the floor. One end of the rope is then shaken. The graph shows the

rope at a particular moment in time. The rope vibrated at a frequency 8 Hz.

Determine

(a) the amplitude

(b) the wavelength

(c) the speed

Solution

Example 4
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The figure shows the sound waves produced by a tuning fork.

(a) Baseon the figure determine,

(i) the amplitude

(ii) the wave length

(b) What is the frequency of the sound if the speed of sound is 330 ms-1.

Solution

Waves on water- Ripple tank

In laboratory, to produce water wave we use a ripple tank.

A shallow tray of clear plastic holds the water, and a light above the water surface projects the wave

patterns on a sheet of white paper on the bench below the tank.

The bright and dark bands of the wave pattern formed on the screen because the surface of water

acts as lenses.


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The crest of water waves similar with convex lens and the trough of water waves similar with

concave lens.

Plane waves are produced by a straight bar which hangs by two elastic bands from supports near

one end of the tank.

Circular waves are produced by using dippers fixed to the bar.

When a continuous stream of waves is used , it is sometimes easier to see by using a mechanical

stroboscope to freeze the wave pattern. When the frequency of the waves same as the frequency of

the stroboscope the pattern will appear stationary.

Stroboscope frequency = number of slits x rotation

frequency of stroboscope or

F=np

Example 5

A mechanical stroboscope has 8 slits and rotates at a frequency 5 Hz. The stroboscope is used to

observe water waves. The observer notes there are 6 successive bright bands at a distance 12 cm.

Calculate the speed of the water waves.

Solution

6.3 Analysing Reflection Wave
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Reflection of waves

Reflection of a wave occurs when a wave strikes an obstacle such as barrier, plane reflector , mirror

and wall.

The reflection of waves obeys the law of reflection :

(a) The angle of incidence is equal to the angle of reflection.

(b) The incident wave, the reflected wave and the normal lie in the same plane.

When the reflection of a wave happened , the wavelength ,, the frequency, f and the speed , v do

not change but the direction of propagation of the wave changes.

Reflection of water waves

To investigate the reflection of water waves a metallic plane reflector is placed at the centre of a

ripple tank. The motor with a wooden bar attached is switched on to produce plane waves which

propagate towards the reflector. The reflector repositioned to produce different angles of incidence.

The following figure shows two examples pattern of the reflection of the water waves.

(a)

Analysis result:

(b)
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Analysis result :

The experiment to investigate the relationship between the angle of incidence and the angle of

reflection of a water wave.

Hypothesis:

The angle of reflection increases as the angle of incidence increases.

Aim of the experiment :

To investigate the relationship between the angle of incidence and the angle of reflection.

Variables in the experiment:

Manipulated variable: Angle of incidence

Responding variable: Angle of reflection

Fixed variable: depth of water in ripple tank

List of apparatus and materials:

Ripple tank, lamp, motor ,wooden bar , power supply white paper , protractor ,plane reflector and

mechanical stroboscope.

Arrangement of the apparatus:

The procedure of the experiment which include the method of controlling the manipulated

variable and the method of measuring the responding variable.

The power supply is switched on to produce plane waves which propagate towards the reflector.
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The incident waves and the reflected waves are freeze by a mechanical stroboscope.

The waves are sketched on the screen.

By using a protractor , the angle of incidence is measured = i and the angle of reflection = r

The experiment is repeated 5 times for the other angles of incidence.

Tabulate the data:

i

r

Analysis the data:

Plot the graph r against i

some analysis of water wave reflection with a different reflector.
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Reflection of light waves

When rays of light strike any surface the rays are reflected , unless the surface is black, when they

are absorbed.

The reflection depend on how smooth the surfaces are. Good mirrors reflect well over 90% of thelight that reaches them, with only a small amount being absorbed.

A plane mirror is a flat smooth surface which reflects regularly most of the light falling on it.

The phenomenon of reflection of light obeys the law

of reflection.

(a) The angle of incidence is equal to the angle of reflection.

(b) The incident wave, the reflected wave and the normal lie in the same plane.

It also can be seen that

(a) The size of the image = the size of the object

(b) The distance of the image = the distance of the object


reflection of a light wave.

Hypothesis:







Fixed variable: position of the plane mirror


Ray box, plane mirror, plasticine, protractor and white paper

Arrangement of the apparatus


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A normal line ,ON is drawn on the white paper.

A ray of light from the ray box is directed to the plane mirror.

By using a protractor , the angle of incidence is measured = i and the angle of reflection = r


Tabulate the data:

i

r

Analysis the data:


Reflection of sound waves

The sound waves is reflected by walls and ceilings of buildings, unborn baby or sea bed.

Echo is a phenomenon when a sound wave has been reflected of a surface , and is heard after the

original sound.


reflection of a sound wave.

Hypothesis:




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Fixed variable: the position of stop watch from the smooth wall.


Cardboard tube, soft wood , stop watch, protractor and smooth wall.

Arrangement of the apparatus:



By using a protractor , the angle of incidence is measured = i

The stopwatch is started.

The cardboard tube B is moved around until the watch can be heard most clearly.

By using the protractor , the angle of reflection is measured = r


Tabulate the data:

i

r

Analysis the data:
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