# Destructive Interference in Water but not Air

• Ichigo449
In summary, the conversation discusses the phenomenon of Rayleigh scattering and how it causes certain sections of the sky to appear dark. It is caused by the superposition of waves from different air molecules, with certain conditions needing to be met for destructive interference to occur. This is true for water, but not for air due to the weight of the air molecules. The conversation also mentions the role of electrical charges in responding to optical waves.

## Homework Statement

Consider a given monochromatic component of sunlight. The electric field drives a given air molecule. Each oscillating charge of the air molecule radiates waves in all directions, some of which travel to the eye of a given observer. But, for a given molecule (call it No.1) there is another (No.2) that is one half-wavelength farther from the observer. If both molecules are driven with the same amplitude and phase constant, their waves should superpose to give zero at the position of the observer. For scattering near ##\frac{\pi}{2}/## radians, we can obviously satisfy these phase and amplitude conditions, provided the number of air molecules per unit volume is large enough so that there is nearly always a molecule "No.2" for every molecule "No.1". So that section of the sky corresponding to the scattering should be dark. This is obviously false for air but, surprisingly, is true for water. Why?
Hint: Consider a small region in space (region 1) and consider another region (region 2) of the same size, situated at the same distance from the sun and situated one half-wavelength (consider a single monochromatic component of sunlight) farther from the observer than region 1. Assume that these regions are small compared with the wavelength. Let there be n1 and n2 molecules in regions 1 and 2 respectively. Compute the total electric field due to these regions and average the amplitude over a single period. Now consider the effect of fluctuations in the number of molecules over a long enough period of time.

## Homework Equations

Coloumb's Law, Conditions for Destructive Interference

## The Attempt at a Solution

I can find the electric fields by Coloumb but am not sure how to include the effects of fluctuations.

I think a molecule is too heavy to respond to an optical wave.

tech99 said:
I think a molecule is too heavy to respond to an optical wave.
It's the electrical charges that need to respond, not the whole molecule. See https://en.m.wikipedia.org/wiki/Rayleigh_scattering.

## 1. What is destructive interference in water but not air?

Destructive interference occurs when two waves meet and their amplitudes cancel out, resulting in a decrease in the overall amplitude. In water, this can happen when two waves with opposite crests and troughs meet, causing the water molecules to move in opposite directions and cancel each other out. However, in air, the molecules are more spread out and cannot easily cancel each other out, so destructive interference is less likely to occur.

## 2. Why does destructive interference happen more in water than in air?

Water is a denser medium than air, meaning there are more molecules packed closely together. This allows for a more efficient transfer of energy and makes it easier for destructive interference to occur. In contrast, air molecules are more spread out and do not interact as closely, making it less likely for destructive interference to happen.

## 3. Can destructive interference be observed in everyday situations?

Yes, destructive interference can be observed in everyday situations. For example, when two waves from different sources meet in a body of water, the resulting pattern of calm and rough water is a result of destructive interference. It can also be observed in light, sound, and other types of waves.

## 4. How does destructive interference affect the overall energy of a wave?

Destructive interference results in a decrease in the overall energy of a wave. When two waves with opposite amplitudes cancel each other out, the combined energy of the wave is reduced. This is why destructive interference is often referred to as "destructive" - it has a diminishing effect on the energy of the wave.

## 5. Are there any real-world applications of destructive interference in water?

Yes, destructive interference in water has several real-world applications. One example is in the construction of harbors and breakwaters. By intentionally creating areas of destructive interference, the energy of incoming waves can be reduced, making it safer for boats to enter and exit the harbor. Destructive interference is also used in some types of water pumps and turbines to reduce overall energy and vibrations.