1.5 Interference

CONTENT : INTERFERENCE OF WAVES CHAPTER HIGHLIGHTS (30 MINUTES)

The principle of superposition When two or more waves meet at the same point, the displacement of resulting wave is equal to the sum of the displacement of the individual waves. 1. Inteference of waves is superposition effects produce by two waves from two coherent point sources.( same frequency, same phase). 2. These two different sources producing nodal lines (consisting of all the points with destructive interference) and anti nodal lines(consisting of all the points with constructive interference). (i) Constructive interference (ii) Destructive interference The fenomena that two identical waves which are in phase ,come together at a point to form a bigger wave.

a

2a

a

=

+

The cancellation of a wave by another when two identical waves which are out of phase come together .

a

+

a

= Zero Displacement

Maximum crest 3.Determination Of Wavelength Using Interference Pattern. screen Anti nodal line

Nodal line Anti nodal line x x

x

Nodal line

Anti nodal line Trough wavefront Peak wavefront

D

Wave length of wave, ax λ= D Where, a = separation between two sources (S1 and S2) of similar wave x = separation between two consecutive antinodal lines or nodal lines D= distance from the source to the position where x is measured.

4. Interference pattern of

Water waves

light waves

a) Constructive interference occurs at the antinode point. Loud sound heard. b) Destructive interference occurs at the node point. Soft sound heard.

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sound waves

a) Constructive interfence occurs at the antinode point. Bright fringes seen b) Destructive interference occurs at the node point. Dark fringes seen.

ACTIVITIES (50 minutes) 1. If two waves meet each other and are in phase, then they interfere to give a __________ amplitude. This is known as ______________. 2. If two waves meet each other and are completely out in phase the they interfere to give a _____________ amplitude. This is known as ____________. 3. State the principle of superposition in the context of interference of two similar waves. ________________________________________________________________ ________________________________________________________________

4. In each wave superposition diagram below, draw the resultant displacement: (a) A

(b)

A

+

+

A

=

=

A

(c) A

+

A =

5. Describe the difference between constructive and destructive interference. ________________________________________________________________ ________________________________________________________________

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6. Name the line joining all the points where constructive interference takes place. Similarly, name the line joining all the points where destructive interference takes place. ________________________________________________________________ ________________________________________________________________ 7. State the condition for the interference pattern of a wave to be observed. ________________________________________________________________ 8. When the light emitted by two headlamps of a car overlaps, will interference be observed? Explain your answer. ________________________________________________________________ ________________________________________________________________ 9. Two loudspeakers are connected to the same signal generator so that the loudspeakers can act as two sources of similar sound waves. What would you hear if you were to walk along in front of these two speakers? ________________________________________________________________ 10. In an experiment, the distance between two sources of vibration is 2.0 cm and the distance between the source of vibration and a screen is 40.0 cm. If the distance between two adjacent lines of antinodes is 8.0 cm, calculate the wavelength of waves produced by the sources of vibration.

Question 12 to 14 are based on the diagram above The diagram shows a double slit and a screen. C is the central fringe, D is the first dark fringe and B is the first bright fringe

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12. State the points that are (a)in phase :____________________________________________________ (b)completely out of phase: ________________________________________ 13.If λ is the wavelength , calculate the difference between (a) S1C and S2C:________________________________________________ (b)S1D and S2D :________________________________________________ (c)S1B and S2B :________________________________________________ 14.Describe the effect of (a)increasing the distance from the slits to C :_________________________ (b)increasing the distance S1S2: ____________________________________ (c)covering up one of the slits:______________________________________ 15.If the slits are 0.4 m apart with the screen 2 m away, and four fringes cover a width of 1.2 cm, find the wavelength.

ASSESMENT (40 MINUTES) 1. Two wave impulses, one with amplitude a and another with amplitude –a travel along a string opposite directions and eventually meet at point O. What is the resultant displacement of the two wave impulses at point O? A. -2a B. 0 C. a D. 2a

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2. The diagram shows the fringe pattern produced from Young’s double slit experiment using the monochromatic red light source.

What happens to the fringes if monochromatic yellow light source is used? A. B. C. D.

the bright fringes are wider than the dark fringes the dark fringes are wider than the bright fringes the distance between consecutive fringes decrease the distance between consecutive fringes increase

3.The diagram shows an interference pattern of two coherent water waves of sources, P and Q. Which of the positions A, B, C or D, does destructive interference occur?

4. In Young’s double slit experiment, red fringes are formed on the screen when a red light red source is used. What will be observed if the red light source is replaced by a blue light source? A. number of fringes decreases B. brightness of fringes increases C. distance between fringes decreases

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5 .The following figure shows pattern of water waves produced when two vibrating dipper S1 and S2 are used as the sources to produce similar waves. Dippers S1 and S2 are both connected to a straight piece of wood which is moved by a motor.

Label constructive interference, destructive interference, nodal line and antinodal line. 6.Figure (a) shows the arrangement of apparatus in Young’s double slit experiment. A white light source is passed through a coloured filter to produce a monochromatic light. Figure (b) shows the pattern of the fringe formed on the screen when a red filter is used. The experiment is repeated by using a blue filter and the fringes formed are shown in Figure (c).

Figure (a)

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(a)What is meant by a monochromatic light? ________________________________________________________________ (b)Using the pattern of the fringes in Figure (a) and (b), state two observations about the distances between consecutive fringes for the red light and blue light. ________________________________________________________________ ________________________________________________________________ (c) Compare the wavelengths of red light to blue light. ________________________________________________________________ (d)Compare the wavelengths of red light and blue light with the distances between consecutive fringes in (b) ________________________________________________________________ (e)Name the wave phenomenon which forms the pattern of the fringes in Figure(a) and (b). ________________________________________________________________

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7.Two similar loudspeakers are placed 0.8m apart. They emit a coherent sound wave. A girl walks slowly parallel to the two loudspeakers at a distance 3.2 m in front of the loudspeakers. She hears a loud sound and weak sound alternately. Figure 2.1 shows the positions of the loud and weak sounds

(a)What is meant by a coherent wave? ________________________________________________________________ (b)The distance between three positions of the loud sound is 4.5 m, as shown in Figure 2.1.Calculate the wavelength of the sound wave.

(c)The loud sound is heard due to the constructive interference of the sound waves. State how the constructive interference occurs. ________________________________________________________________ ________________________________________________________________

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ANSWERS OF ACTIVITIES 1. bigger,constructive interference 2. zero, destructive interference 3.When two waves pass a point at the same time, the resultant displacement of the wave at that point is the sum of the displacements of the individual waves 4.(a)

(b)

(c)

2A

- 2A

5.The difference is the amplitude of the resultant wave. Constructive interference produces bigger wave and destructive interference produces no waves 6. antinodal line, nodal line 7. Two sources of similar waves are placed near each other 8.No.Each car head lamp is made up of many light sources 9.Alternate of loud and soft sound can be heard 10. 4 x 10 -3 m 12.(a)C and B (b)D 13.(a) 0 (b) 1/2 λ (c) λ 13. (a)the distance between the fringes will increase (b)the distance between the fringes will decrease 14. 6 x 10 -7 m ANSWERS OF ASSESMENT 1.B 2.C 3.D 4.C 5..

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6(a)Monochromatic light is a light of one colour or one wavelength source. (b)i. the distance between consecutive fringes of the same light source are the same ii. the distance between consecutive fringes of the red light are greater than the blue light (c) the wavelength of the red light is greater than the blue light (d) the greater the wavelength, the greater the distance between consecutive fringes. (e)interference 7.(a)coherent wave is defined as waves with the same wavelength and frequency ax 4.5 (b)λ= x= D 2 0.8(2.25) = = 2.25 m 3.3 = 0.55 m (c)crest meets crest/trough meets trough

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