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6.6 Interference Of Waves

Interference of waves

When two or more travel in the same or different directions in a given space, variations in the size of the resulting disturbance occur at points where the meet or overlap.

Interference is the superposition of two waves originating from two coherent sources.

Two waves are in coherent if they are of  the same frequency, same amplitude and in phase (same phase)

There are two types of interference :

(a)     Constructive interference occurs when the crests or troughs of both waves coincide to produce a wave with maximum amplitude.

(b)      Destructive interference occurs when the crests of one wave coincide with the trough of the other waves  to produce a wave with zero amplitude.

Interference of the waves  is a result or obeys the principle of superposition.

Principle of  superposition 

Principle of  superposition state that “ When two waves move simultaneously and coincide at a point the sum of  the displacements at that point is  equal to the sum of the displacements of the individual waves by vector method”.

(a)           Superposition of two crests

                clip_image002

Constructive interference

Constructive interference  is  a point at which  two crest coincide.

(b)   Superposition of two troughs 

clip_image004 

Constructive interference

Constructive interference  is  a point at which  two trough coincide.

(c)   Superposition of a crest and a trough 

    clip_image006

Destructive interference       

Destructive interference  is  a point at which  a crest and a trough coincide

Analysing Interference of water waves 

To produce the interference pattern of the water waves in a ripple tank we can use:

(a)  Two dippers operated from the same motor,

                clip_image008

                                                                Or

(b)           A plane water waves passing through two slits.

clip_image010 Activity : Interference

clip_image012

clip_image014 

The figure shows the interference pattern produced by  two sources of water  P and Q.

1.      A cross (x)  in the figure is the points where the crests coincide crests.

2.      Mark with a star  (clip_image015)  in the figure is the points where the troughs coincide troughs .

          The points  (x)  and   (clip_image015)  is called as constructive interference.

          constructive interference is a point where two crest coincide or  two trough coincide.

At that points constructive interference occurs.

clip_image017

3.      A circle ()  in the figure is the points where a crest coincide with a trough.

          The points   ()  is called as   Destructive Interference.

          Destructive Interference is a point where the total displacement is  zero.

          At the points Destructive Interference occurs.

clip_image019

4.      Connect the points (x)  and   (*)  to produce several lines that we call as  node  lines

5.      Connect the points () to produce several lines that we call as  antinode  lines

clip_image0216.The value of  l   can be calculated from   clip_image023          where :                               

            λ = wavelength

                a = source separation

                x = distance between two successive constructive interference or   Destructive  Interference

      D = distance between source and screen.

How to change the pattern of interference of waves?

The pattern of interference depends on the distances between two consecutive nodes or antinodes lines , x.

How to change x ?

From the formula clip_image026

                                Hence  clip_image028

Conclusion  :                       As λ increases , x increases

                                                As D increases , x increases

                                                As a increases , x  decreases

clip_image030

                                                As λ increases , x increases

clip_image032                                                As a increases , x  decreases

The experiment to investigate the relationship between the distance between to coherent sources  and the distance between two consecutive node lines

Hypothesis:

The distance between two consecutive node lines

increases  as  the distance between to coherent sources   decreases

Aim of the experiment :

To investigate the relationship between the distance between to coherent sources   and the distance between two consecutive node lines

Variables in the experiment:

Manipulated variable: the distance between to coherent sources

Responding variable: the distance between two consecutive node lines

Fixed variable: frequency of vibrator or  the wavelength

List of apparatus and materials:

Ripple tank,  lamp, motor ,wooden bar , power supply ,white paper , spherical dippers ,metre rule  and mechanical stroboscope.

Arrangement of the apparatus:

clip_image034

The procedure of the experiment which include the method of controlling the manipulated variable and the method of measuring the responding variable.

By using a metre rule , the distance between two dippers is measured = a

The power supply is switched on to produce two circular waves from the dippers

The waves  are freeze by a mechanical stroboscope.

The waves are sketched on the screen.

By using the metre rule , the distance between two consecutive node lines is measured = x

The experiment is repeated 5 times for with different  distances between two dippers

Tabulate the data:

 a

 

 

 

 

 

 

 x

 

 

 

 

 

 

Analysis the data:

 Plot the graph  x against  a

clip_image036

Example 1 

 In an experiment to investigate the pattern interference of a water waves, the distance between two spherical dippers is 2.5 cm and the distance between two consecutive antinodes lines is 5.0 cm. What is the wavelength of the water waves if when the distance from two dippers to the point of measurement is 10 cm.

Solution

 

Interference of light waves 

When light from the same source passes through two narrow slits  which are close

together the effect known as interference can be seen as the bright and dark fringes.

The bright fringes to be formed by constructive Interference and the dark fringes to be

formed by destructive interference.

clip_image038

Interference fringes produce by using Double-slit

interference Young’s experiment.

For all practical purposes, monochromatic light is used.

Monochromatic light  which is light of only one colour or one wavelength.

The formula for interference of light waves is, clip_image026

Where,

                λ = wavelength of light waves

                a = slit separation

                x = distance between two successive bright or dark fringes

      D = distance between double slit and screen.

Example 2

 In a double-slit interference experiment with blue light the distance between the screen and double slit  is 1.2 m and slit separation is  2 x 10-4 m .  Six successive bright fringes  at a distance 1.2  x 10 -2 m is formed on the screen. Calculate the wavelength of the blue light.

Solution

 

The experiment to investigate the relationship between the wavelength of the light waves distance and the distance between two consecutive bright fringes

Hypothesis:

The distance between two consecutive bright fringes

increases  as  the wavelength of light waves increases.

Aim of the experiment :

To investigate the relationship between the wavelength of the light waves distance and the distance between two consecutive bright fringes

Variables in the experiment:

Manipulated variable:  The wavelength of the light waves( colour of light)

Responding variable: the distance between two consecutive bright fringes

Fixed variable: slit separation and  the distance between double slit and screen.

List of apparatus and materials:

Source of light,colour filter, screen, single slit, double slit  and metre rule.

Arrangement of the apparatus:

clip_image040

The procedure of the experiment which include the method of controlling the manipulated variable and the method of measuring the responding variable.

A green filter is placed between the light source and the slits.

The source of light is switched on.

The interference  pattern formed on the screen is observed and drawn.

By using a metre rule the distance across  6 consecutive bright fringes is measured.

The distance between two consecutive bright fringes is calculated ,

clip_image002

The experiment is repeated 5 times for with different  colour filters

Tabulate the data:

 λ

 

 

 

 

 

 

 x

 

 

 

 

 

 

Analysis the data:

 Plot the graph  x against  λ

clip_image042 

The arrangement of colour of light in order of wavelength

clip_image044

Interference of sound waves

Like other types of waves ,sound waves can also give interference effects. Interference of sound waves produce regions of louder sound by constructive interference and regions  quiet by destructive interference.

When two similar loudspeakers are connected to the same audio-frequency  generator they will produce interference effects.

The formula for interference of sound waves is,

clip_image026

Where,

                λ = wavelength of sound waves

                a = distance between two loudspeakers

                x = distance between two successive loud regions or quiet region.

      D = distance between the listener from the loudspeaker.  

Example 3

In an experiment on the interference of sound wave a listener at distance 5.0  from the loudspeaker. The distance between two loudspeakers is 2.0 m. The loudspeakers are connected to an audio-frequency  generator to produce sound waves at a frequency of 0.8 kHz.

Calculate

(a)     the wavelength of sound waves when the speed of sound is 320 ms-1

(b)     the distance between two successive loud regions

Solution:  

The experiment to investigate the relationship between distance of  the listener from the loudspeaker  and the distance between two successive loud regions

Hypothesis:

the distance between two successive loud regions increases  as distance between the listener from the loudspeaker increases .

Aim of the experiment :

To investigate the relationship between distance between the listener from the loudspeaker  and the distance between two successive loud regions

 Variables in the experiment:

Manipulated variable: Responding variable: distance between the listener from the loudspeaker

Responding variable: the distance between two successive loud regions

Fixed variable: the wavelength of sound waves , distance between two loudspeakers

List of apparatus and materials:

Two loudspeakers, audio-frequency  generator ,connection wires and metre rule.

Arrangement of the apparatus:

clip_image046

The procedure of the experiment which include the method of controlling the manipulated variable and the method of measuring the responding variable.

By using a metre rule the distance between the listener from the loudspeaker is measured= D

The audio-frequency  generator is switched on.

The listener is requested to walk in a straight path and the distance between  two successive loud regions is measured by a metre rule = x

The experiment is repeated 5 times for with different distances between the listener from the loudspeaker

Tabulate the data:

 D

 

 

 

 

 

 

 x

 

 

 

 

 

 

Analysis the data:

 Plot the graph  x against  D

clip_image048

2 Responses

  1. […] 6.6 Interference Of Waves March 2010 1 comment […]

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