# How To Calculate Wavelength

# How To Calculate Wavelength

**Wavelength Formula: **Wavelength is the stretch between the crests of a wave. Many extraordinary things can move like waves, like strings, water, the air (noise waves), the ground (earthquakes), and light can be treated as a wave. Wavelength is represented with the Greek letter lambda: λ. It is equal to the velocity of the wave, divided by the prevalence. Wavelength is expressed in units of meters (m).

Wavelength is the area of 1 frequency wave peak to the other and is most commonly associated with the electromagnetic gamut.^{} Calculating wavelength is dependent simultaneous the information you are given. If you know the speed and frequency of the wave, you can use the basic formula for wavelength. If you want to determine the wavelength of light given the specific energy of a photon, you would use the energy comparison. Calculating wavelength is easy as long as you know the correct equation.

## Formula For Wavelength

There are three main properties of a wave its acceleration, wavelength and frequency.

**Wave velocity (v)** is the project of how fast does a wave propagate in a given medium. Its unit is meter per second. Check the speed calculator for more informations about speed and velocity.

**Wavelength (λ)** is the distance over which the shape of wave repeats. It depends on the medium a wave travels through. It is measured in meters.

**Frequency (f)** of a wave refers to how many times (per a given time period) do the particles of a medium vibrate when the wave is running through it. The unit of recurrence is Hertz, or 1/second.

### Wavelength formula

The relationship between wavelength and frequency is portrayed by this simple equation:

`λ = v/f`

Remember about respectable units! If in trouble, you can always use the speed conversion.

### How to calculate the wavelength

It’s easy! Just use our wavelength calculator in the following way:

- Regulate the frequency of the wave. For example,
`f = 10 MHz`

. This frequency belongs to the radio waves spectrum. - Choose the velocity of the wave. As a delinquency, our calculator uses a value of
`299 792 458 m/s`

– the speed of light propagating in the air. - Replace these values into the wavelength equation
`λ = v/f`

. - Calculate the result – in this example, wavelength will be equal to
`29.98 m`

. - You can also use this tool as a frequency computer. Simply type in the values of momentum and wavelength to obtain the result.

Remember that the frequency doesn’t change when passing from one medium to another. If you are solving a complex trouble with more than one medium, use the wavelength custom again with the same frequency, but different velocity.

## Wavelength Frequency Formula

Ripples in water, sound trekking in air, and harmonized vibrations of objects are examples of waves you have probably encountered in your life. A good way to visualize a wave is to insert the end of a pencil into a container of still water. The surface of the water is disturbed, producing ripples, or waves.

Electromagnetic waves are special waves, such as light, radio waves, microwaves, and x-rays, that do not compel a medium for propagation. We cannot see or hear these waves, but they exist in nature and in many of the products we use every day.

Regardless of the kind, every wave has a wavelength. **Wavelength** is the distance between two successive like marks on a wave. Some examples are the distance between two stream peaks or two adjacent valleys. A **peak** is the highest point of a wave and a **valley** is the lowest point of a wave. Stated another way, wavelength is the time required to complete one full cycle of the wave.

Wavelength depends on two other important parameters:

### 1. Wave Speed

The rate at which the wave moves through the medium of propagation. Wave speed is dependent upon the medium of propagation. For example, water ripples travel through the water. Electromagnetic waves usually travel through the air, as do sound waves. Vibrations on a piano string travel through the string. The wave speed is different for all of these because the medium in which the wave propagates is different.

### 2. Frequency

The number of wave cycles passing a point per unit time. Stated another way, it is the number of oscillations per second in the wave. A higher frequency means a shorter wavelength, and a shorter wavelength means a higher frequency. This leads us to the relationship between wave speed, frequency, and wavelength. The speed of the wave equals the number of cycles passing a point each second multiplied by the cycle length. Mathematically stated: wave speed = cycles per second x cycle length

## De Broglie Wavelength Formula

It is equal to the velocity of the wave, divided by the frequency. Wavelength is expressed in units of meters (m).

*λ* = wavelength, the distance between wave crests (m)

*v* = wave velocity, the speed that waves are moving in a direction (m/s)

*f* = frequency, the wave crests that go through a point in a certain time (cycles/s or Hz)

Wavelength Formula Questions:

1) The speed of sound is about *340 m/s*. Find the wavelength of a sound wave that has a frequency of *20.0* cycles per second (the low end of human hearing).

Answer: The wave velocity *v = 340 m/s*, and the frequency *f = 20.0 cycles/s*. The wavelength ? can be found using the equation:

*λ = 17.0 m*

The wavelength of the sound is 17 meters.

2) A motor boat makes waves that travel across the surface of a lake. The waves travel toward shore at a velocity of *1.50 m/s*. The distance between wave crests is *2.00 m*. What is the frequency of the waves?Answer:: The wave velocity *v = 1.50 m/s*, and the wavelength *λ = 2.00 m*. The frequency must be solved for, so rearrange the equation:

*f = 0.75 waves/s*

The frequency of these water waves is *0.75* waves per second.

## Frequency Wavelength Formula

**Plug the known quantities into the equation and solve.** If you want to calculate the wavelength of a wave, then all you have to do is plug the wave’s speed and wave’s frequency into the equation. Dividing speed by frequency gives you the wavelength.^{}

- For example: Find the wavelength of a wave traveling at 20 m/s at a frequency of 5 Hz.
- {\displaystyle Wavelength={\frac {Wavespeed}{Frequency}}}

{\displaystyle \lambda ={\frac {v}{f}}}

{\displaystyle \lambda ={\frac {20m/s}{5Hz}}}

{\displaystyle \lambda =4m}

- {\displaystyle Wavelength={\frac {Wavespeed}{Frequency}}}

**Use this equation to solve for speed or frequency.** You can rearrange this equation and solve for speed or frequency if given wavelength. To calculate speed given frequency and wavelength, use {\displaystyle v={\lambda }*{f}}. To calculate frequency given speed and wavelength, use {\displaystyle f={\frac {v}{\lambda }}}.^{}

- For example: Find the speed of a wave with wavelength 450 nm and frequency 45 Hz. {\displaystyle v={\lambda }*{f}={450nm}*{45Hz}=20,250nm/s<=20.25um/s}.

For example: Find the frequency of a wave with wavelength 2.5 m and speed 50 m/s. {\displaystyle f={\frac {v}{\lambda }}={\frac {50m/s}{2.5m}}=20Hz}

## How does light wavelength affect photosynthesis?

The **best wavelengths of light for photosynthesis** are those that **are blue (375-460 nm) and red (550-700 nm)**. These wavelengths are absorbed as they have the **right amount of energy to excite electrons in the plant’s pigments**, the first step in photosynthesis. This is **why plants appear green**, because red and blue light that hits them is absorbed!

## What is the relationship between frequency and wavelength?

Frequency (f) and wavelength (λ) are joined by the equation **fλ= c**, where c is the speed of light. As the speed of light is constant, if you increase the frequency, the wavelength must decrease to maintain this equation, and vice versa. This means that the relationship between **frequency and wavelength is inversely proportional**.

## What color is the longest wavelength?

**red, with a wavelength of ~700 nm**. The wave with the longest wavelength,

**radio waves**, cannot be seen by the human eye, and therefore

**doesn’t have a color**. The colour of the shortest wavelength is violet, at about 400 nm.