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Destructive interference is a phenomenon that occurs when two waves come together and entirely cancel each other out.
- Interference of waves is a phenomenon that occurs when two coherent waves combine by adding their intensities or displacements.
- Depending on how the two waves interact, the resulting wave may have more intensity or less amplitude.
- Waves can interfere in two ways: Constructive interference and Destructive interference.
- Constructive interference occurs when two waves are in phase with each other.
- Destructive interference occurs when two waves are totally out of phase.
| Table of Contents |
Key Terms: Waves, Interference, Young’s Single Slit Experiment, Frequency, Huygens' guideline, amplitudes
Wave Interference
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Interference occurs when two waves (travelling through the same place) superimpose to generate a new wave of larger or lesser amplitude.
- The result of two or more wave trains flowing in opposite directions on a crossing or coinciding path.
- The effect is the sum of the individual wave amplitudes at each site where more than one wave is present.
- Interference effects are represented in all forms of waves including radio, light, surface water waves and acoustic.
- When two waves collide, their amplitudes mix, resulting in interference.
There are two types of wave interference:
- Constructive interference
- Destructive interference
Constructive interference takes place at the time when the maxima of two waves add together so that the amplitude of the resulting wave is equivalent to the sum of the individual amplitudes.
Also Read:
| Related Articles | ||
|---|---|---|
| Wave Theory of Light | Carnot engine | Huygens Principle |
| Doppler Effect Formula | NCERT Solutions Chapter 10 Electric Charges and Fields | Interference of light waves and young's experiment |
Destructive Interference
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The destructive interference occurs when the maxima of the two waves are 180 degrees out of phase and a positive displacement of one wave is cancelled exactly by a negative displacement of the other wave.
- When the first wave rises, the second wave descends, and the two waves sum up to zero.
- They add to zero again when the first wave is down and the second is up.
- In fact, the two waves perfectly cancel each other out at all times, leaving no wave.
- This is the single most incredible feature of waves.
- The aggregate of two waves can be less than either wave individually or even zero.
The presence of at least two waves is the most critical criterion for interference.
- Interference occurs when waves with the same frequency and amplitude superimpose on each other.
- Because of their superposition, when two waves of comparable frequency move in a medium at the same time and in the same direction, the resulting intensity of the medium at any place differs from the total of their intensities.
- The strength of the resulting wave has a larger value at some spots, while it has a very small value at others.
What is Destructive Interference?
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“If two or more waves are traveling in a medium, the resulting wave function is the algebraic total of the individual waves function.”
When two waves of comparable frequencies move in a medium, the resultant at various sites differ from the sum of their intensities because of their superposition. We call it Destructive Interference when it is too little and inconsequential at one point.
Equations of Destructive Interference
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- When the phase difference between two waves is an odd multiple of π:
| (2n-1) π |
- When the difference in a path between two waves is an odd multiple of λ /2:
| Δ = (2n-1) λ /2 |
- When Between the two waves the time gap is an odd multiple of T/2:
| θ = (2n-1) T/2 |
Examples of Destructive Interference
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Some of the examples of destructive interference are given below:
- The noise-cancelling headphones function by playing a sound that has the opposite amplitude as the incoming sound, causing the two sound waves to destructively interfere and cancel each other out.
- Destructive Interference is also caused by moving electrons and radio waves.
- Destructive Interference is demonstrated with light beams.
- Gravity waves are also an example of destructive interference.
Things to Remember
- Interference is a wave interaction phenomenon, when two waves collide at a point, they cause interference. The two waves cancel out in destructive interference, resulting in decreased amplitude at the point where they meet.
- The largest absolute value of a varying quantity is called amplitude.
- When two stones are put into a pool of water, waves from each source spread out, causing interference where they contact.
- The superposition of two waves with slightly different frequencies but identical amplitudes produce beats.
- The ear's function is to convert the signals in bouncing air molecules into electrical nerve signals while maintaining as much information as possible in the signals.
- Ships can utilise sound waves to navigate by transmitting sound waves and measuring the time between transmissions and receiving the reflection. This is referred to as sonar.
- Destructive interference is only effective for a short period of time. Where the displacement of the medium is smaller than the displacement of the wave with the maximum amplitude.
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Sample Questions
Ques. What methods do you use to identify destructive interference? (1 Mark)
Ans. The standard formula for destructive interference caused by a path difference is ? = (2n-1) λ /2.
Ques. When destructive interference occurs then what is lost? (1 Mark)
Ans. The magnetic energy is lost by destructive interference, but the electric energy is doubled.
Ques. How can you tell whether interference is destructive or constructive? (2 Marks)
Ans. The difference in wavelengths for constructive interference will be an integer number of whole wavelengths. It will be a digit number of whole wavelengths plus a half wavelength for destructive interference.
Ques. How electromagnetic waves are generated? (2 Marks)
Ans. Electromagnetic waves forms when the accelerating charges and transferring charges back and forth produces oscillating electric and magnetic fields that travel at the speed of light.
Ques. What is destructive interference path difference? (2 Marks)
Ans. The path difference between the two waves is half a wavelength; in other words, the path difference is 0.5. For path differences of half a wavelength, destructive interference emerges.
Ques. What is interference? (2 Marks)
Ans. Interference occurs when two waves (travelling through the same place) superimpose to generate a new wave of larger or lesser amplitude. the result of two or more wave trains flowing in opposite directions on a crossing or coinciding path. The effect is the sum of the individual wave amplitudes at each site where more than one wave is present. Interference effects are represented in all forms of waves including radio, light, surface water waves and acoustic. When two waves collide, their amplitudes mix, resulting in interference.
Ques. What are the types of wave interference? (1 Mark)
Ans. There are two types of wave interference:
- Constructive interference
- Destructive interference
Ques. Which of the following does not show any interference pattern? (2 Marks)
a. A thick film
b. Soap bubble
c. Wedge Shaped film
d. Excessively thin film
Ans. The correct answer is d. Excessively thin film
Explanation: An interference pattern does not appear in an exceedingly thin film because, because the thickness of the film is small, the path difference,Δ, between the two reflected rays is λ/2, which is the condition of minima. As a result, the pattern is not detected. In the soap bubble, thick film, and wedge-shaped film, the interference pattern is seen.
Ques. The main principle used in Interference is (2 Marks)
a. Quantum Mechanics
b. Heisenberg’s Uncertainty Principle
c. Superposition Principle
d. Fermi Principle
Ans. The correct answer is c. Superposition Principle
Explanation: The main concept used in light interference is the superposition principle. When incoming light waves superimpose constructively, the intensity increases; when they superimpose destructively, the intensity drops.
Ques. What is destructive interference? (1 Mark)
Ans. Destructive interference is just a type of interference that can happen anywhere along the medium where two interfering waves have opposing displacements.
Ques. What is constructive interference? (1 Mark)
Ans. Constructive interference occurs when two waves overlap so that they combine to form a larger wave.
Ques. State the principle of superposition. (2 Marks)
Ans. The superposition principle states that when two or more waves overlap in space, then the resultant disturbance is equal to the algebraic sum of the individual disturbances.
Ques. Write some examples of destructive interference. (2 Marks)
Ans. Some of the examples of destructive interference are given below:
- The noise-cancelling headphones function by playing a sound that has the opposite amplitude as the incoming sound, causing the two sound waves to destructively interfere and cancel each other out.
- Destructive Interference is also caused by moving electrons and radio waves.
- Destructive Interference is demonstrated with light beams.
Ques. Write down two conditions in order to obtain the sustained interference fringe pattern of light. State the effect on the interference fringes in Young’s double slit experiment, when monochromatic source is replaced by a source of white light? (Foreign 2008)
Ans. The conditions for sustained interference are:
(i) The two sources of light need to be coherent in order to emit light of constant phase difference.
(ii) The amplitude of electric field vector of interfering wave must be identical so that it can have greater contrast between intensity of constructive and destructive interference.
When monochromatic light is replaced by white light, the coloured fringe pattern will be appeared on the screen.
Ques. Write the importance of coherent sources in the phenomenon of interference. In Young’s double slit experiment to produce interference pattern, find out the conditions for constructive and destructive interference. Therefore, deduce the expression for the fringe width. If the entire experimental apparatus of YDSE is immersed in water, how does the fringe width get affected? (All India 2011)
Ans. In order to observe interference fringe pattern, there must have coherent sources of light which can produce light of constant phase difference.
Let two coherent sources of light S1 and S2 are derived from a source S. These two slits S1 and S2 are equidistant from source S. now, suppose S1 and S2 are divided by distance d. The slit and screen are distance D apart.
Assuming any arbitrary point P on the screen at a distance yn from the centre O. the path difference between interfering waves is S2P - S1P.
For the constructive interference:
Path difference = nλ, where, n = 0, 1, 2,...
dyn/D = nλ (from equation i)
→ yn = Dnλ/d
→ yn+1 = D(n +1)λ/ d
β = Dλ /d(n+ 1) - Dnλ/ d = dλ/ d (n + 1 - n) = Dλ/ d
Fringe width of dark fringe, β = Dλ /d … (ii)
For destructive interference:
Path difference = (2n - 1) λ/2, where n = 1, 2, 3,...
→ Y’nd/ D = (2n - 1) λ/2 (from equation i)
→ Y’n = (2n - 1) Dλ/ 2d
Where Y’n is the separation of nth order dark fringe from central fringe.
Therefore, Y’n+1 = (2n +1) Dλ/ 2d
→ β = Y’n+1 - Y’n
(ii) Here in this case, the light of blue colour interfere destructively. Therefore, this colour would substract from white light. Thus, yellow colour fringe would be obtained at P.
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