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Chapter 7: Problem 7

Explain the meaning of the term interference.

Short Answer

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Answer: Interference is the phenomenon where two or more waves superimpose to produce a resultant wave with a changed amplitude. Constructive interference occurs when waves are "in phase," meaning their crests and troughs align, resulting in a higher amplitude. Destructive interference occurs when waves are "out of phase," meaning the crest of one wave aligns with the trough of another, resulting in a lower amplitude or canceling each other out.

Step by step solution

01

Definition of Interference

Interference refers to the phenomenon in which two or more waves superimpose to produce a resultant wave of greater, lower, or the same amplitude. It occurs when waves from different sources combine to produce a combined effect. Interference can be either constructive, resulting in an increased amplitude, or destructive, resulting in a decreased amplitude.
02

Constructive Interference

Constructive interference happens when two or more waves meet in such a way that their crests line up together, as well as their troughs. This causes the resultant wave to have a higher amplitude than the individual waves. In other words, the waves are said to be "in phase" with each other. For example, consider two waves with the same amplitude and frequency traveling in the same direction along a rope. If these waves meet at a certain point, their combined amplitude will be the sum of the individual amplitudes (i.e., twice the amplitude of either wave).
03

Destructive Interference

Destructive interference occurs when two or more waves meet in such a way that the crest of one wave coincides with the trough of another wave. This results in the waves canceling each other out, producing a combined wave with a lower amplitude. In other words, the waves are said to be "out of phase" with each other. For example, consider the same two waves from the previous example, but this time the crest of one wave meets the trough of the other wave. In this case, the combined amplitude of the resultant wave is the difference between the individual amplitudes (i.e., potentially zero, if both waves have equal amplitudes). In summary, interference refers to the phenomenon in which two or more waves combine to produce a resultant wave with a changed amplitude. The outcome can be either constructive or destructive, depending on the alignment of the waves' crests and troughs.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Constructive Interference
When studying waves, it's fascinating how two or more waves can come together to create something entirely new. Constructive interference is one of these interesting phenomena. It occurs when waves combine in such a way that their crests (the highest points) and troughs (the lowest points) align perfectly. This alignment leads to a superposition where the amplitude of the resulting wave is greater than any of the individual waves. Think of it as waves "helping" each other to become bigger.

This happens because the waves are "in phase," meaning they are synchronized in their up and down motion. Imagine two friends jumping on a trampoline at the same time and in the same rhythm; their combined efforts make them jump higher together than they would alone.
  • The amplitudes add up to create a stronger wave.
  • The waves maintain their original shape but with increased height.
  • Constructive interference typically happens when the path difference between the waves is a multiple of their wavelength.
Destructive Interference
Destructive interference, like its name suggests, involves waves that "destroy" or diminish each other's effects. This happens when the crest of one wave aligns with the trough of another, effectively canceling each other out. The result is a wave with a smaller amplitude or, in some cases, no wave at all!

In scientific terms, these waves are said to be "out of phase," meaning their peak movements don't match. For instance, if two people are on a seesaw, with one going up while the other goes down, their movements oppose one another.
  • The waves cancel each other out, reducing the overall amplitude.
  • When the amplitudes are equal but opposite, they can completely nullify each other's effect.
  • Destructive interference occurs when the path difference is a half multiple of the wavelength, like half, one and a half, etc.
Wave Superposition
Wave superposition is the foundational concept behind both constructive and destructive interference. It's the principle that waves can overlay one another to form a new wave pattern. This principle is what allows multiple waves to exist in the same space and interact with each other, creating the effects we observe with interference.

Think of wave superposition as mixing colors; when you combine different paints, you get new shades. Similarly, when waves overlap, they create patterns based on their combined amplitudes:
  • If waves align perfectly, they can amplify each other (constructive interference).
  • If waves are out of sync, they can reduce or cancel each other out (destructive interference).
  • This ability to overlap without altering the fundamental way a wave travels is unique to wave behavior.
Wave superposition showcases how waves are fundamentally different from particles, highlighting the unique behavior that makes studying wave dynamics so interesting.

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Most popular questions from this chapter

Why is a 50 percent recovery of single-crossover products the upper limit, even when crossing over always occurs between two linked genes?

Are sister chromatid exchanges effective in producing genetic variability in an individual? in the offspring of individuals?

In a series of two-point map crosses involving five genes located on chromosome II in Drosophila, the following recombinant \((\sin -\) gle- crossover) frequencies were observed:$$\begin{array}{lr} p r-a d p & 29 \\ p r-v g & 13 \\ p r-c & 21 \\ p r-b & 6 \\ a d p-b & 35 \\ a d p-c & 8 \\ a d p-v g & 16 \\ v g-b & 19 \\ v g-c & 8 \\ c-b & 27 \end{array}$$ (a) If the adp gene is present near the end of chromosome II (locus 83 ), construct a map of these genes. (b) In another set of experiments, a sixth gene ( \(d\) ) was tested against \(b\) and \(p r,\) and the results were \(d-b=17 \%\) and \(d-p r=23 \% .\) Predict the results of two-point maps between \(d\) and \(c, d\) and \(v g,\) and \(d\) and \(a d p\)

What three essential criteria must be met in order to execute a successful mapping cross?

Why does more crossing over occur between two distantly linked genes than between two genes that are very close together on the same chromosome?
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