Frequency, also known as wave frequency, is the measure of the total number of vibrations or oscillations produced in a given time. There are a few different ways to calculate frequency based on the information you have at your disposal. Read on to learn some of the most common and useful versions out there.
Steps
Method 1 of 4: Calculate the Wavelength Frequency
Step 1. Learn the formula
The formula for calculating the frequency, when you know the wavelength and the speed of the wave, is expressed as follows: f = V / λ
- In this formula, f represents the frequency; V, the speed of the wave; and λ, the wavelength.
- Example: a certain sound wave traveling through air has a wavelength of 322 nm when the speed of sound is 320 m / s. What is the frequency of this sound wave?
Step 2. Convert the wavelength to meters if necessary
If the wavelength is given in micrometers, you will need to convert this value to meters by dividing it by the number of micrometers in a meter.
- Keep in mind that when you are working with extremely small or extremely large numbers, it is generally easier to write these values using scientific notation. The values in this example may or may not be expressed in scientific notation, but when you are writing the answer for your homework, other school papers, or other formal forums, it would be best to use scientific notation.
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Example: λ = 322 nm
322 nm x (1 m / 10 ^ 9 nm) = 3.22 x 10 ^ -7 m = 0.000000322 m
Step 3. Divide the velocity by the wavelength
Divide the speed of the wave, V, by the wavelength converted to meters, λ, to find the frequency, which is f.
Example: f = V / λ = 320/0, 000000322 = 993788819, 88 = 9, 94 x 10 ^ 8
Step 4. Write your answer
After completing the previous step, you will have your wave frequency calculation ready. Write your answer in Hertz, Hz, which is the unit used to express units of frequency.
Example: the frequency of this wave is 9.94 x 10 ^ 8 Hz
Method 2 of 4: Calculate the Frequency of Electromagnetic Waves in Vacuum
Step 1. Learn the formula
The formula for calculating the frequency of a wave in vacuum is almost identical to that of a wave that does not occur in a vacuum. Since there are no external influences that affect the speed of the wave, you should use the mathematical constant of the speed of light, in which electromagnetic waves travel under these conditions. In this way, the formula will be expressed like this: f = C / λ.
- In this formula, f represents the frequency; C, the speed of light; and λ, the wavelength.
- Example: A particular wave of electromagnetic radiation has a wavelength of 573 nm when it travels through a vacuum. What is the frequency of this electromagnetic wave?
Step 2. If necessary, convert the wavelength to meters
If the problem gives you the wavelength in meters, you don't need to do anything else. However, if the wavelength is in micrometers, you need to convert this value to meters by dividing it by the number of micrometers in a meter.
- Keep in mind that when you are working with extremely small or extremely large numbers, it is generally easier to write these values using scientific notation. The values in this example may or may not be expressed in scientific notation, but when you are writing the answer for your homework, other school papers, or other formal forums, it would be best to use scientific notation.
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Example: λ = 573 nm
573 nm x (1 m / 10 ^ 9 nm) = 5.73 x 10 ^ -7 m = 0.000000573
Step 3. Divide the speed of light by the wavelength
The speed of light is a constant, so even if the problem doesn't give you a value, it will always be 3.00 x 10 ^ 8 m / s. Divide this value by the wavelength converted to meters.
Example: f = C / λ = 3, 00 x 10 ^ 8/5, 73 x 10 ^ -7 = 5, 24 x 10 ^ 14
Step 4. Write your answer
With this, you will have already calculated the value of the wave frequency. Write your answer in Hertz, Hz, which is the unit used to express units of frequency.
Example: the frequency of this wave is 5.24 x 10 ^ 14 Hz
Method 3 of 4: Calculate the Frequency of Time or a Period
Step 1. Learn the formula
The frequency and the time it takes for a single wave oscillation to complete are inversely proportional. In this way, the formula to calculate the frequency when they give you the time necessary to complete the cycle of a wave is written like this: f = 1 / T
- In this formula, f represents the frequency and T represents the period or amount of time required to complete the oscillation of a single wave.
- Example A: The time it takes for a single wave to oscillate is 0.32 seconds. What is the frequency of this wave?
- Example B: In 0.57 seconds, a certain wave can make 15 oscillations. What is the frequency of this wave?
Step 2. Divide the number of oscillations by the time period
They will usually tell you how long a single swing takes to complete, in which case you just need to divide the number
Step 1. between the time period, T. However, if they give you the amount of time it takes several swings to complete, you will need to divide the number of swings by the total time it takes to complete them.
- Example A: f = 1 / T = 1/0, 32 = 3, 125
- Example B: f = 1 / T = 15 / 0.57 = 26.316
Step 3. Write your answer
This calculation should tell you the frequency of the wave. Write your answer in Hertz, Hz, which is the unit used to express units of frequency.
- Example A: the frequency of this wave is 3.15 Hz.
- Example B: the frequency of this wave is 26.316 Hz.
Method 4 of 4: Calculate the frequency from an angular frequency
Step 1. Learn the formula
If you are given the angular frequency of a wave, but not the standard frequency of that same wave, the formula for calculating the standard frequency will be written like this: f = ω / (2π)
- In this formula, f represents the frequency of the wave and ω represents the angular frequency. As with any mathematical problem, π stands for pi, a mathematical constant.
- Example: a particular wave rotates with an angular frequency of 7.17 radians per second. What is the frequency of that wave?
Step 2. Multiply pi by two
In order to find the denominator of the equation, you will need to double the value of pi, which is 3.14.
Example: 2 * π = 2 * 3, 14 = 6, 28
Step 3. Divide the angular frequency by twice pi
Divide the angular frequency of the wave, expressed in radians per second, by 6.28, which is the doubled value of pi.
Example: f = ω / (2π) = 7, 17 / (2 * 3, 14) = 7, 17/6, 28 = 1, 14
Step 4. Write your answer
This portion of the final calculation should tell you what the frequency of the wave is. Write your answer in Hertz, Hz, which is the unit used to express units of frequency.