1.5 interference

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CHAPTER 1: WAVES1.5 Analysing Interference of Waves

PRINCIPLE OF SUPERPOSITION

• 1 The Principle of superposition states that at any instant, the wave displacement of the combined motion of any number of interacting waves at a point is the sum of the displacements of all the component waves at that point.

• The principle of superposition states that the when two /more waves meet at a certain point, the resultant displacement at that point is the vector sum of the individual waves

• 2 Figures 1.46 (a), (b) and (c) show the combined amplitude produced when two waves, both of amplitude a, from opposite directions meet.

• 3 Interference pattern is a result of the superpositions of waves.

When two or more waves meet, they superpose or combine at a particular point. The waves are said to interfere.

INTEFERENCE OF WAVES

INTERFERENCE OF WAVES

• 1 Interference is the superposition of two waves originating from two coherent sources. Sources which are coherent produce waves of the same frequency (f), amplitude (a) and in phase.

Wave B

Wave A

• 2 The superposition of two waves emitted from coherent sources gives either constructive or destructive interference.

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

• 4 Destructive interference occurs when the crest of one wave coincides with the trough of the other wave, thus canceling each other with the result that the resultant amplitude is zero

• 5 Figure 1.47 shows the occurrence of constructive interference and destructive interference.

• 6 An antinode is a point where constructive interference occurs, whereas a node is a point where destructive interference occurs. From Figure 1.48, it can be seen that the antinodes line joins all antinodes while the node lie joins all nodes.

• Experiment 1.8 : To investigate the interference of water waves

(I) Different wavelengths ( )

• Problem statementWhat is the relationship between the wavelength, , and the distance between two adjacent node lines (or antinode lines), x, in the interference pattern?

• Hypothesis

The distance between two adjacent node lines (or antinode lines), x, increases as the wavelength increases.

• Variables:• (a) Manipulated:Frequency of the dippers or

wavelength• (b) Responding: Distance between two

consecutive node lines, or, antinode lines (x)

(I) Different wavelengths ( ) (c)Fixed Variables:

(i) Distance between two sources (a)(ii) Distance from sources to the point where the distance between two adjacent node lines or antinode lines (x) is measured (D)

• (I) Different wavelengths ( )

• Apparatus/Materials

• Ripple tank, spherical dippers and mechanical stroboscope.

• (I) Different wavelengths ( ) • Procedure• 1 A ripple tank is set up with two spherical

dippers in contact with the surface of the water.• 2 The distance between the two spherical

dippers is fixed at 4 cm.

• (I) Different wavelengths ( ) • Procedure• 3 The motor and the rheostat are adjusted to

operate the motor at low frequency.• 4 The pattern of the interference of the waves

is observed with a stroboscope and the pattern is drawn.

• 5 Steps 3 and 4 are repeated with the vibrator operating at a higher frequency. The waves produced have a shorter wavelength.

Low fHigh f

• Observation

• Discussion

• 1 Table 1.2 shows that when the two waves combined to produce waves of larger amplitude as shown by the regions which are bright (where the crests of the two waves coincide) and the darker regions (where the troughs coincide). This part of the pattern of waves shows the crests and troughs which are reinforced as a result of constructive interference.

• Discussion

• 2 In some regions where the water is still, without any ripples, the crests and troughs of the two waves coincide and eliminate each other (destructive interference). Since the amplitude is zero, there is no wave motion.

• 3 The results in Table 1.7 shows that when the frequency is higher, i.e., the wavelength is shorter, the distance between two adjacent node lines or antinode lines, x, is smaller.

• Conclusion

• The distance between two consecutive node lines or node lines (x) increases when the wavelength of the water waves ( ) from the source increases.

• Conclusion

The hypothesis is valid.

• (II) Different distances between the two sources of waves (a)

• How is the distance between the two sources of waves, a, related to the distance between two adjacent node lines or antinode lines, x, in the interference pattern?

• Hypothesis

• If the distance between two sources of waves, a, is decreased, the distance between two consecutive node lines or antinode lines, x, increases.

• Variables• (a) Manipulated : Distance between the two sources (a)• (b) Responding: Distance between the two consecutive

node, or antinode lines (x)• (c) Fixed:• (i) Frequency of dippers (f) or wavelength ()• (ii) Distance from sources to the point where the

distance between two adjacent node, or antinode lines (x) is measured (D)

• Apparatus/Materials

• Ripple tank, Spherical dippers, metre rule and mechanical stroboscope

• Procedure• 1 The ripple tank is set

up as shown in Figure 1.49.• 2 The distance between

two spherical dippers, a, is fixed at 4 cm.

• 3 The motor is switched on and the rheostat is adjusted to obtain waves with medium wavelength.

• Procedure• 4 The interference

pattern is observed with stroboscope and the pattern is drawn.

• 5 Steps 3 and 4 are repeated with the distance between the two spherical dippers reduced to 2 cm

• Observations

• Conclusion

• The distance between two consecutive node (or antinode) lines, x, is inversely proportional to the distance between the two sources.

• The hypothesis is valid.

RELATIONSHIP BETWEEN , A, X AND D

• Keys:• a = distance between two coherent sources • = wavelength• x = distance between two consecutive node (or

antinode)lines• D = distance from the two sources to the point of

measurement of x

• From the interference pattern (Figure 1.52) and factors that influence the interference pattern in Experiment 1.8, we found that

• Example 10

• In the interference of two coherent sources of waves, the separation between two spherical dippers is 3 cm and the distance between two consecutive node lines is 4 cm measured at a distance of 15 cm from the two coherent sources of waves. Calculate the wavelength of the water waves originating from the sources.

• Example 10

• Solution

• Substituting a = 3 cm, x = 4 cm, D = 15 cm into the formula

• = 0.8 cm

INTERFERENCE OF LIGHT WAVES

• 1 Interference of light waves, like that of water waves and sound waves, also requires two coherent sources.

• 2 Waves emitted from two coherent sources have the same frequency (or wavelength) and in phase.

• 3 Light emitted by a single source consists of waves which extend over a wide range of wavelengths and are not in phase. Because of this, it is difficult to have two sources of light which are coherent.

• 4 In 1801, Thomas Young produced two coherent light sources in his experiment now referred to as Young's double-slit experiment.

• 5 Principle of Young's double-slit experiment:

• (a) Yellow light emitted by a sodium-vapour lamp has a very narrow frequency band. For all practical purposes, it can be considered as monochromatic light which is light of only one frequency or wavelength.

• Figure 1.53 Young's double-slit experiment

• (b) Slits S1, and S2 give rise to two coherent light sources since the light passing through them are from the same monochromatic light, the sodium-vapour lamp.

• (c) Interference occurs as a result of the superposition of the two light waves originating from S1 and S2. A pattern consisting of a series of parallel and alternating bright and dark fringes is formed.

• (d) The bright fringes are regions where constructive interference occurs, whereas the dark fringes are regions of destructive interference.

• (e) Figure 1.54 shows the interference pattern obtained in Young's double-slit experiment.

• Figure 1.54

• (f) The widths of the bright and dark fringes are the same.

INTERFERENCE OF SOUND WAVES

1. When coherent sound waves propagate from two loudspeakers of 2 m apart, an observer can hear the loudest sound. The loudspeakers are connected to a source waves with a frequency of 500 Hz and observer walks a distance of 10 m in front of the loudspeakers. If the speed of sound is 300 ms-1, what is the distance between two consecutive loudest sounds heard by the observer?

QUIZ: Interference and refraction

Diagram below shows the interference pattern of water waves.Rajah dibawah menunjukkan corak interferen gelombang air.

What happens to the separation between two consecutive nodal lines, x, if thedepth of water in the ripple tank is increased?

Apakah yang akan berlaku kepada jarak pemisahan 2 garisan nodal berturutan, x, jika kedalaman air dalam tangki riak meningkat?

A. Unchanged / Tidak berubah B. Increase / Bertambah C. Decrease / Berkurang

53Factors affecting interference patternFactors affecting interference pattern

D α x1. D x

2. λ x λ α x

3. a ↓ x

a α 1 x

x = Dλ a

1.5 interference

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