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6.1 Vibration And Wave

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.

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Amplitude :

The maximum displacement of the objects from their equilibrium position.

Period, T

The time taken for one complete oscillation.

The S.I. unit is second (s)

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t = time

n = number of oscillations

Frequency, f

The number of complete oscillations per second.

The S.I. unit is Hertz (Hz)

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Or

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Graph displacement-time

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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

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Oscillation of a spring hang with a mass

Spring constant

mass

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Oscillation of a jigsaw blade fixed with plasticine ball

jigsaw contant

mass

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Transformation of energy in a vibration system.

image

What is meant by Resonance?

A phenomenon that occurs when the frequency of forced vibrations on an object matches the object’s natural frequency and a dramatic increase in amplitude results.

Experiment to show a phenomenon of resonance

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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:

image

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:

image

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:

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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 :

image

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.

Example 6 :

image

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 :

image

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.

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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.

2 Responses

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