Wavelength is the distance of one frequency wave peak to the other. The calculation of wavelength depends on the information. You need to know the frequency and speed of the wave. By using the formula, the wavelength can be calculated. Calculating the wavelength is easy if you know the correct equation. So, in this guide, we have explained the definition and how to find wavelength.
The meaning of wavelength is the distance from a crest to another or from one trough to another. It is denoted by lambda (λ). It can be electromagnetic, sound, or any other. In this scenario, the highest point is the crest and the lowest points is the trough.
In essence, it is measured in:
- kilometers
- meters
- millimeters
- micrometers
Furthermore, it can also be measured in smaller denominations, like
- nanometers
- picometers
- Femtometers
Main Properties Of Waves
Different properties characterize waves.
Amplitude: The maximum displacement of points on a wave, measured from the equilibrium position. It determines the wave’s energy and intensity. Therefore, it measures in meters.
Wavelength: It measures the distance between 2 consecutive points on a wave in meters. Usually, it is denoted by the lambda (λ).
Velocity: Defines the speed at which a wave passes via a medium. Therefore, it is calculated as the product of frequency and wavelength.
Period: It takes time for one complete cycle to pass a given point. T is denoted by it and measured in seconds or minutes.
Frequency (f): The last one is frequency. It defines the number of wave cycles that pass a point in a fixed time. It is measured in Hz, equal to 1 wave/second.
Wavelength Formula
The formula for calculating wavelength is λ = v/f.
- λ is the wavelength,
- v is wave speed, and
- f is frequency
In meters (m) is typically measured a wavelength, in meters per second is the velocity, and in Hz is the frequency measured. The Greek letter lambda (λ) represents a wavelength.
Energy To Wavelength Formula
- Wave speed equation
- Planck-Einstein relation
The equation is:
V = f x λ
Where:
v= wave speed in m/s
f= frequency of the wave in s
λ= wavelength in m
Next is the Planck-Einstein relation:
E= hxf
Where:
E= photon energy in J
h= Planck’s constant, equal to 6.62607015×10−34 J Hz−1
f= frequency of the wave in s
Furthermore, you can practice the problems in MyMathLab to excel in it.
How To Calculate Wavelength?
Below are the steps that need to be followed while calculating wavelength:
Firstly, calculate the wavelength with the wavelength equation. However, to find the wavelength, divide teh speed of the wave by frequency. The formula to calculate is:
wavelength= wave speed/frequency
Secondly, use the correct units. We represent speed using imperial and metric units. Therefore, it is expressed as km/h, miles/h, meters/h, and others. Metric units, such as m, nm, mm, and others, are used to express wavelength. Frequency is expressed in Hertz, signifying a rate of one cycle per second.
In the third step, plug the known quantities to solve the equation. After that, when calculating the wave’s wavelength, plug the speed and frequency, then divide the speed by frequency.
Example:
To find the wavelength of a wave, you can use the formula:
λ=v/f
Where:
- λ is the wavelength,
- v is the velocity of the wave,
- f is the frequency of the wave.
Given:
- v=30 m/s
- f=6 Hz
Now, plug in the values:
So, the wavelength of the wave is 5 meters.
The equation is used to solve for the frequency or speed. In addition, the equation can be rearranged and used to find the speed or frequency if wavelength is given. However, to calculate speed from wavelength and frequency, use the equation v = fxλ. To calculate the frequency from wavelength and speed, use the equation f = v/λ.
You can also use MyOpenMath to learn and practice math concepts.
Example:
To find the wavelength with energy, you can use the following relationship between energy and wavelength, which is derived from the Planck-Einstein relation:
E=hc/λ
where:
So, the wavelength of the photon is approximately 5.26 μm (micrometers).
The equation can also be used to determine the maximum wavelength of light necessary to ionize metals.
What Are The Steps To Catch Mistakes?
Check the answer by multiplying wavelength by frequency. When the correct wavelength value is found, we can determine the wave speed by multiplying it by the frequency. Hence, if you don’t get it, double-check the calculation. While using the calculator, make sure the numbers are typed correctly.
Example:
To find the wavelength of a sound wave, you can use the formula:
λ=v/f
where:
- λ is the wavelength,
- V is the speed of the wave,
- F is the frequency of the wave.
Given:
- v=443 m/s
- f=80 Hz
Now, plug in the values:
So, the wavelength of the 80 Hz sound wave travelling at 443 meters per second is 5.5375 m.
To check the answer by multiplying the wavelength by the frequency:
λxf= 5.5375 m x 80 Hz
λxf= 443m/s
Since multiplying the wavelength by the frequency gives us the original speed of the wave, the calculation is correct.
Secondly, we use scientific notation to avoid calculator rounding errors. Often, wavelength calculation involves large numbers, especially when working with light speed. Thus, this can lead to rounding errors on the calculator. So, writing the numbers in scientific notation can prevent this and double-check the significant digits.
Example:
To find the wavelength of light traveling through water, you can use the formula:
λ=v/f
where:
- λis the wavelength,
- v is the speed of light in water,
- F is the frequency of the light.
Given:
So, the wavelength of the light traveling through water is 6.5×10−7 m or 650 nanometers.
Thirdly, do not change the frequency when a wave enters a different medium. Henceforth, you will get many word problems involving waves that cross the boundary from one medium to another. In addition, many people make the common mistake of calculating a new frequency for the wave. However, when the wave crosses the boundary, the frequency remains the same while the speed and wavelength change.
Lastly, check the units. Meanwhile, the units tell what to do when solving a problem. Thereupon, when finished, if they don’t make sense, check if you have used the correct units. For example, if you use Joules(J) when you have to use Hz, you will get an incorrect answer.
In addition, if you face difficulty understanding it, you can also take an online class.
Typical Wave Speeds
Below are a few typical wave velocity values:
- Light in air or vacuum: 299,792,458 m/s
- Light in water: 224,901,000 m/s
- Sound in air: 343.2 m/s
- Sound in water (20 °C): 1,481 m/s
Frequently Asked Questions
How Do I Calculate Energy From Wavelength?
To calculate the energy:
- Convert your wavelength into meters(m).
- Divide the speed of light by the wavelength in m. It gives you the wave’s frequency.
- Multiply the frequency by Planck’s constant. The result is the wave energy in joules (J).
How Do You Calculate Wavelength From Energy?
- Convert photon’s energy into Joules
- Divide the light speed by the photon’s energy
- Multiply the result by Planck’s constant
- Then, find the photon’s wavelength in m
How Wavelength And Frequency Are Related?
They are related by the equation fλ = c. Here, c is the speed of light. The latter is constant, so the wavelength must decrease if you increase the frequency. Therefore, it is essential to maintain the equation and vice versa.
Can I Find The Wavelength Of Any Wave With Distance?
Yes, you can use the formula λ = d/n,
where
- λ is the wavelength,
- d is the distance, and
- n is the number of waves.
To calculate the wavelength, including sound and electromagnetic waves. Moreover, the distance should be the same as the wavelength measured.
How Can I Calculate Wavelength Without Frequency?
Calculate the wavelength with only distance, which requires frequency or the number of waves. Hence, you need to know the frequency to get the correct wavelength.
How Do We Find Frequency From Wavelength?
- You should convert SI units for frequency or wavelength if necessary.
- Solve the equation for the desired variable using the formula v=fλ
- Then, substitute the velocity values for frequency or wavelength to solve for the desired quantity.
How Can Wavelength Affect Photosynthesis?
It affects the efficiency & rate of photosynthesis. It also influences the light energy that plants use. Therefore, different wavelengths of light trigger other responses in plants:
- Red light (600–700 nm): The main driver of vegetative growth and has the highest net photosynthetic rate
- Blue light (400–500 nm): Helps form chlorophyll, promoting healthy leaf and stem growth and increasing the roots’ ratio to plant development.
- Greenlight (500–600 nm): Weakly absorbed compared to red and blue wavelengths but plays an increasingly important role in overall photosynthesis potential.
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