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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.

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.

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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.

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An example of transerve waves is sound waves..

Wave terminology

Amplitude:

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

Period , T:

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.

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Wavelength , λ

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.

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Or

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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.

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circular wavefront

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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

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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.

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Determine

(a) the amplitude

(b) the wavelength

(c) the speed

Solution

Example 4

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

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(a) Base on 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

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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.

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

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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.

image

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

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