# How to Calculate the Amplitude of a Resultant Electromagnetic Wave?

• thereddevils
In summary, the electric components E1 and E2 of two coherent electromagnetic waves are given as E_1=E_o\sin (\omega t-kx) and E_2=E_o\sin (\omega t-k(x+\delta)). The amplitude of the resultant wave can be derived by using the identity for the sine of the difference of angles, and can be expressed as A\sin (\omega t-k(x+\alpha)). The phase constant alpha can be determined by using this identity, along with the amplitude A, which can be found in terms of E0 and delta.
thereddevils

## Homework Statement

The electric components E1 and E2 of two coherent electromagnetic waves are given as follows :

$$E_1=E_o\sin (\omega t-kx)$$

$$E_2=E_o\sin (\omega t-k(x+\delta))$$

These two waves superpose each other at a certain point . Derive the amplitude of the resultant wave in terms of k and delta .

## The Attempt at a Solution

I tried adding them using the sin formulas , but i failed to express it in the form of

$$A \cos \theta \sin \omega t$$

The sum of the two waves can be substituted by a single one of the same angular frequency w and wavenumber k, that is

$$E_o\sin (\omega t-kx)+E_o\sin (\omega t-k(x+\delta))= A\sin (\omega t-k(x+\alpha))$$.

You have to find the expression of A in terms of E0 and delta.

ehild

ehild said:
The sum of the two waves can be substituted by a single one of the same angular frequency w and wavenumber k, that is

$$E_o\sin (\omega t-kx)+E_o\sin (\omega t-k(x+\delta))= A\sin (\omega t-k(x+\alpha))$$.

You have to find the expression of A in terms of E0 and delta.

ehild

thanks ehild , but i don really get it , i don see where is the alpha coming from ..

Alpha is a phase constant for the new wave. You can determine both alpha and the amplitude A by using the identity for the sine of the difference of angles. Have you learned how to do it?

ehild

## 1. What are electromagnetic waves?

Electromagnetic waves are a type of energy that is created by the movement of electrically charged particles. These waves are composed of both electric and magnetic fields and can travel through a vacuum or through different types of matter.

## 2. What are the properties of electromagnetic waves?

Electromagnetic waves have several key properties, including wavelength, frequency, amplitude, and speed. Wavelength is the distance between two consecutive peaks or troughs in the wave, while frequency is the number of complete waves that pass a given point in one second. Amplitude is the height of the wave, and speed is how fast the wave travels through a medium.

## 3. How are electromagnetic waves produced?

Electromagnetic waves are produced when an electrically charged particle, such as an electron, is accelerated or decelerated. This creates a disturbance in the electric and magnetic fields, which then propagate outward as electromagnetic waves.

## 4. What is the electromagnetic spectrum?

The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. It includes all types of electromagnetic waves, from low frequency radio waves to high frequency gamma rays. The different types of electromagnetic waves have varying properties and uses.

## 5. How are electromagnetic waves used in everyday life?

Electromagnetic waves have a wide range of uses in everyday life. Radio waves are used for communication, microwaves are used for cooking, infrared radiation is used in remote controls and thermal imaging, visible light allows us to see, ultraviolet radiation is used in medical treatments, X-rays are used in medical imaging, and gamma rays are used in cancer treatment. Additionally, electromagnetic waves are used in technology such as cell phones, Wi-Fi, and satellite communication.

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