Question

Describe the relationship between the wavelength and frequency of electromagnetic waves.

Answer 1

The relationship between frequency and wavelength is that they are inversely proportional.

Step-by-step explanation:

For instance, we can treat a wave with a higher frequency on a rope faster than before. While doing this, we'll notice that the wavelength will become shorter. Thus, the relation between frequency and wavelength do exist, so let’s find out what exactly is this relationship.

Period (T) is another entity that can be used to describe a wave. It is defined as the time taken to complete oscillation. However, since frequency determines the number of times a wave oscillates and it can be expressed as,

f = 1/t

Now, since a wave undergoes one oscillation during one period, every point on the wave returns to the same value after one period. This is as a result of every session of oscillation travelling a distance of a wavelength in one period to finish.

Now, wave speed (v) is defined as the distance travelled by a wave per unit time. If we consider that the wave travels a distance of one wavelength in one period, it is given by the formula ;

ν=λ/T

Where λ is wavelength.

As we know that, T = 1/f, hence we can express the above equation as,

V = f λ

Now, at a value of wave velocity, as the frequency is increasing, the wavelength would be decreasing and this implies the relationship between frequency and wavelength is that they are inversely proportional.

Answer 2

Frequency and wavelength are inversely proportional and the higher the frequency, the higher the energy of the electromagnetic wave.

Step-by-step explanation:

Electromagnetic waves are transverse waves formed by an electric field and a magnetic field perpendicular to it. They propagate in a vacuum since the variation on an electric field generates a magnetic field and vice versa.

The electromagnetic spectrum is the distribution of radiation due to the different frequencies at which it radiates and its different intensities.

Radiation is distributed along that electromagnetic spectrum according to the wavelength or frequency. For example, X-rays, ultraviolet rays, the visible region are the ones with the highest frequencies and infrared, microwave and radio waves with lower frequencies.

However, the velocity of an electromagnetic wave can be defined as:

`c = \\u \cdot \lambda` (1)

Where c is the speed of light,
`\\u` is frequency and
`\lambda` is the wavelength.

Therefore, if
`\lambda` or
`\\u` are isolated in equation 1, is easy to see that one is inversely proportional to the other.

`\\u = (c)/(\lambda)` (2)

For example, in equation 2 when the frequency increases the wavelength decreases.

The energy of the electromagnetic wave can be determined by means of the following equation:

`E = h\\u` (3)

Where h is the Planck's constant and
`\\u` is the frequency.

Hence, frequency and energy are directly proportional.

Equation 2 can be replace in equation 3:

`E = (hc)/(\lambda)` (4)

Then, energy and wavelength are inversely proportional