What is the relationship between frequency and wavelength of light

Light is a form of electromagnetic radiation, which are the fields that are associated with light energy. Light is a very general term as it can be referred to as anything from a simple light bulb to microwaves. Some properties of light include wavelength and frequency. Frequency (typically measured in Hertz) is the number of waves in a specific time. Wavelength (typically measured in nanometers) is the distance between two points in a wave. Frequency and wavelength have both direct and inverse relationships. For instance, if two waves are traveling at the same speed, they are inversely related. The wave with shorter wavelength will have a higher frequency while a longer wavelength will have a lower frequency. This is represented in the picture below.

Frequency and wavelength can be related through the speed of light. Light moves with the speed of 3.00 x 108 meters per second. Speed of light, frequency, and wavelength can all be expressed in an equation. λν=c f is solved for c, speed of light. v represents frequency and λ represents wavelength. As mentioned previously, this is an inverse relationship because as one of the values goes up, the other value goes down. With this basic equation, you can also solve for wavelength and frequency to get their equations as well. 

Just as wavelength and frequency are related to light, they are also related to energy. The shorter the wavelengths and higher the frequency corresponds with greater energy. So the longer the wavelengths and lower the frequency results in lower energy. The energy equation is E = hν. E represents energy, h represents Planck's constant (6.626 x 10-34 J · s), and v represents frequency. The energy equation is a direct relationship between frequency and energy because as frequency increases, so does energy. This is possible because h is a constant. 

Here is a sample problem of finding energy: How many kg/mol of energy are there in a photon with λ = 550nm?

In step 1 of solving the problem, you need to identify the equation in which you will be using. In this problem, I used the energy equation because it is asking for the amount of energy. I then plugged in numbers. We know Planck's constant but we are also given the wavelength when there is no variable for wavelength in the energy equation. How will we solve this problem?

In step 2, I used the wavelength to find frequency. I used the equation for speed of light. Once I solved for frequency in the light equation, I plugged in the numbers that were given. We know the speed of light and we also know the wavelength because it is given in the problem. Although the wavelength is given in nm, I converted it to m so it is easier to solve for later in the problem. To convert nm to m, I divided 550 nm by 10-9. The frequency is then found after plugging in the speed of light and wavelength.

In step 3, I plugged in Planck's constant and the frequency found in step 2 into the energy equation. This is not the final answer because it is in Joules when the problem asks for kilojoules per mole. 

In step 4, I identified Avogrado's number. This is used to find kilojoules for one mole. I then multiplied Avogrado's number by the energy in Joules that was found in step 3.

In the final step, I converted the answer I got in Joules per mole into kilojoules per mole. To do this, I multiplied the answer I got in step 4 by .001 kJ (or you can divide by 1000 kJ) to get this final answer as 217.5 kJ/mol. 

Light can have many different forms and properties. Wavelength and frequency are the most basic properties that can be both directly and inversely related. The speed of light equation shows an inverse relationship between wavelength and frequency because as one values increases, the other value decreases. On the other hand, the energy equation shows a direct relationship because as frequency increases, so does energy. 

Source:

A wave is defined as a disturbance in a material that transports energy without causing net particle movement. They travel in a periodic, repeated motion, transferring energy from the source to the destination. Waves are divided into two types: transverse waves and longitudinal waves. Transverse waves are light and water waves while longitudinal waves are sound and compression waves.

What is the frequency?

The number of oscillations of a wave per unit of time is defined as frequency (Hz). It is the reciprocal of time and is represented by the sign f. Its unit of measurement is hertz. Its dimensional formula is [M0L0T-1].

What is wavelength?

The distance between the two closest points in phase with each other is specified as a wavelength. It’s represented by the symbol (lambda). It is the product of a wave’s distance travelled per unit time and the total time taken. Its unit of measurement is meters. Its dimensional formula is written as [M0L1T0].

Relation Between Frequency And Wavelength

The frequency and wavelength are indirectly proportional to each other. More is the wavelength, lesser is the frequency and vice-versa. The speed at which a wave travels is equal to the product of its frequency and wavelength, which justifies the link between these two parameters.

V = λ f

where,

V is the wave speed,

f is the wave frequency,

λ is the wavelength.

Derivation

The relation between the frequency and wavelength can be derives using the formulas for these two quantities.

We know that frequency is the time taken to complete one oscillation out of time t. So we have,

f = 1/t      …….. (1)

Also, it is known that the speed of a wave is the ratio of distance travelled by the wave to the total time taken by it.

V = λ/t

V = λ (1/t)

Using (1) we get,

V = λ f

This derives the relation between frequency And wavelength of a wave.

Sample Problems

Problem 1. Calculate the wave frequency if a wave completes one cycle in 0.02 s.

Solution:

We have,

Time (t) = 0.02 s

Using the formula we have,

f = 1/t

f = 1/0.02

f = 50 Hz

Problem 2. Calculate the wavelength of a wave travelling at the speed of 250 m/s and has a frequency of 600 Hz.

Solution:

We have,

V = 250,

f = 600

Using the formula we have,

V = λ f

=> 250 = λ (600)

=> λ = 250/600

=> λ = 5/12

=> λ = 0.416 m

Problem 3. Calculate the wavelength of a wave travelling at the speed of 32 m/s and has a frequency of 800 Hz.

Solution:

We have,

V = 32,

f = 800

Using the formula we have,

V = λ f

=> 32 = λ (800)

=> λ = 32/800

=> λ = 1/25

=> λ = 0.04 m

Problem 4. Calculate the frequency of a wave travelling at the speed of 70 m/s and has a wavelength of 2 m.

Solution:

We have,

V = 70,

λ = 2

Using the formula we have,

V = λ f

=> 70 = 2f

=> f = 70/2

=> f = 35 Hz

Problem 5. Calculate the frequency of a wave travelling at the speed of 135 m/s and has a wavelength of 10 m.

Solution:

We have,

V = 135,

λ = 10

Using the formula we have,

V = λ f

=> 135 = 10f

=> f = 135/10

=> f = 13.5 Hz

Problem 6. Calculate the time taken by a wave for travelling a distance of 0.2 m at the speed of 350 m/s.

Solution:

We have,

V = 350,

λ = 0.2

Using the formula we have,

V = λ f

=> 350 = 0.2 f

=> f = 350/0.2

=> f = 1750 Hz

Find the time taken by using the formula f = 1/t.

t = 1/f

= 1/1750

= 0.00057 s

Problem 7. Calculate the velocity of a wave that travelled a distance of 2.5 m in 8 s.

Solution:

We have,

λ = 2.5,

t = 8,

Find the frequency by using the formula,

f = 1/t

= 1/8

= 0.125 Hz

Using the formula we have,

V = λ f

V = (2.5) (0.125)

V = 0.3125 m/s

What is relationship between frequency and wavelength?

What is the relationship between energy frequency and wavelength of light?