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### Course: Class 11 Physics (India)>Unit 19

Lesson 3: Wave interference

# Constructive and Destructive interference

Constructive interference happens when two waves overlap in such a way that they combine to create a larger wave. Destructive interference happens when two waves overlap in such a way that they cancel each other out. Wave interference also depends on the relative phase of the two waves, as this video shows through the examples of path length differences and pi shifts. Created by David SantoPietro.

## Want to join the conversation?

• How is energy conserved in destructive interference?
• This is a great question.
The short answer is energy is always conserved and the "missing" energy caused by the destructive interference is redistributed to the regions of constructive interference. If the waves perfectly cancel in all regions, then the energy of the wave is redirected back to the source.
• what if the waves have different frequencies , i guess the they would not be be coherent . so then how will interference be?
• the superposition rule always applies. The waves of different frequencies when collide do not form a completely constructive or destructive interference but at some points constructive and at some points destructive. look for more at the beat section. hope this helps! vote up!
• Is it possible to conduct a simple constructive and destructive interference experiment with sound?
• yes, ofc dude
When two or more sound waves occupy the same space, they affect one another. The waves do not bounce off of each, but they move through each other. The resulting wave depends on how the waves line up. Two identical sound waves can add constructively or destructively to give different results.
(1 vote)
• What is the difference between coherent waves and identical waves?
• Identical waves are just waves with the same waveform, amplitude, frequency, speed, wavelength, etc.
Coherent waves are identical waves with a constant phase difference.
• What does David mean when he talks about a Consine Wave?
(1 vote)
• Cosine wave: its a 2D representation of 2 varying quantities. It has a phase difference of pi/2 when compared to Sine wave. At a given instant, Cosine wave lags/ leads the sine wave by pi/2.
You can know more in detail (formulae, representation etc.) about it in the internet under the topics: Trignometry, sinusoidal waveforms.
Cosine and Sine waves are pretty important mathematical representations finding applications in various subjects.
• Are there examples of this happening in a real-life scenario like in water? or sonar? If there is, could you explain how the waves would interact especially how it would affect the amplitude, period, and phase?
• Noise canceling headphones use destructive interference to minimize noise. These headphones have a microphone and detect external sounds and produce sound waves that are out of phase with the incoming sound to decrease its intensity.
• Just wanted to confirm if this is the formula for finding phase difference of a wave:
Δϕ=(2π÷λ) × Δx

Δϕ is phase difference.
λ is the wavelength.
Δx is the path difference as given in the video.
• Yes, the phase difference is as you've shown, Δϕ = (2π/λ) * Δx.
• Are we assauming that the wavelenght of the two waves are same? Sorry if its a stupid question but otherwise superstition doesn't make sense to me.
(1 vote)

when the waves meet, they will interfere. so...There will be an interference pattern.

if the waves are coherent (ie constant phase difference) then the pattern will be stationary

if they are not coherent (eg wavelengths NOT the same length) there will be a pattern but it will change. ir the pattern is dynamic...

ok??

put simply, if you want a stationary diffraction pattern, then yes, the wavelengths will need to be the same.
if the wavelengths are not the same, the waves can still interfere. but the pattern will fluctuate.

ok??