Frequency, also called wave frequency, is a measurement of the number of vibrations or oscillations that occur in a given time interval. There are several different ways to calculate frequency based on the information you have. Keep reading to learn about some of the most used and useful versions.
Step
Method 1 of 4: Frequency from Wavelength
Step 1. Learn the formula
The formula for frequency, given the wavelength and speed of the wave, is written as f = V /
- In this formula, f represents the frequency, V represents the speed of the wave, and represents the wavelength.
- Example: A certain sound wave traveling through air has a wavelength of 322 nm and the speed of sound is 320 m/s. What is the frequency of this sound wave?
Step 2. Convert the wavelength to meters, if needed
If the wavelength is known in nanometers, you need to convert this value to meters by dividing by the number of nanometers in one meter.
- Note that when working with very small or very large numbers, it is usually easier to write the values in scientific notation. For this example, the values will be changed to and from the scientific notation for this example, but when writing your answers to homework, other schoolwork, or other official forums, you must use scientific notation.
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Example: = 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, but convert the wavelength to meters,, to find the frequency, f.
Example: f = V / = 320 / 0, 000000322 = 993788819, 88 = 9, 94 x 10^8
Step 4. Write down your answers
After completing the previous steps, you will complete your calculations for the frequency of the waves. Write your answer in Hertz, Hz, which is the unit of frequency.
Example: The frequency of this wave is 9.94 x 10^8 Hz
Method 2 of 4: Frequency of Electromagnetic Waves in a Vacuum
Step 1. Learn the formula
The formula for the frequency of a wave in a vacuum is almost the same as for the frequency of a wave in a vacuum. Because even though there is no outside influence affecting the speed of the wave, you will be using a mathematical constant for the speed of light, which electromagnetic waves propagate under these conditions. Thus, the formula is written as: f = C /
- In this formula, f represents the frequency, C represents the speed or speed of light, and represents the wavelength.
- Example: A certain electromagnetic wave radiation has a wavelength of 573 nm as it passes through a vacuum. What is the frequency of this electromagnetic wave?
Step 2. Convert the wavelength to meters, if needed
If it's a matter of giving the wavelength in meters, you don't need to do anything. However, if the wavelength is given in micrometers, you must convert this value to meters by dividing by the number of micrometers in one meter.
- Note that when working with very small or very large numbers, it is usually easier to write the values in scientific notation. For this example, the values will be changed to and from the scientific notation for this example, but when writing your answers to homework, other schoolwork, or other official forums, you must use scientific notation.
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Example: = 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 its wavelength
The speed of light is a constant, so even if the problem doesn't give you a value for the speed of light, it will always be 3.00 x 10^8 m/s. Divide this value by the wavelength converted to meters.
Example: f = C / = 3.00 x 10^8 / 5, 73 x 10^-7 = 5, 24 x 10^14
Step 4. Write down your answers
With this, you can calculate the frequency value of the waveform. Write your answer in Hertz, Hz, the unit for frequency.
Example: The frequency of this wave is 5.24 x 10^14 Hz
Method 3 of 4: Frequency of Time or Period
Step 1. Learn the formula
Frequency is inversely proportional to the time it takes to complete one wave vibration. Thus, the formula for calculating the frequency if you know the time it takes to complete one cycle of the wave, is written as: f = 1 / T
- In this formula, f represents the frequency and T represents the time interval or the amount of time it takes to complete one wave vibration.
- Example A: The time it takes for a given wave to complete one vibration is 0.32 seconds. What is the frequency of this wave?
- Example 2: In 0.57 seconds, a wave can make 15 vibrations. What is the frequency of this wave?
Step 2. Divide the number of vibrations by the time interval
Usually, you will be told how long it will take to complete one vibration, in which case, you just need to divide the number
Step 1. with time interval, T. However, if you know the time interval for several vibrations, you must divide the number of vibrations by the total time interval required to complete all the vibrations.
- Example A: f = 1 / T = 1 / 0, 32 = 3, 125
- Example B: f = 1 / T = 15 / 0.57 = 26, 316
Step 3. Write down your answers
This calculation will tell you the frequency of the wave. Write your answer in Hertz, Hz, the unit of frequency.
- Example A: The frequency of this wave is 3.125 Hz.
- Example B: The frequency of this wave is 26, 316 Hz.
Method 4 of 4: Frequency of Angular Frequency
Step 1. Learn the formula
If you know the angular frequency of a wave, and not the ordinary frequency of the same wave, the formula for calculating the ordinary frequency is written as: f = / (2π)
- In this formula, f represents the frequency of the wave and represents the angular frequency. Like any math problem, represents pi, a mathematical constant.
- Example: A certain 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
To find the denominator of the equation, you must multiply the values of pi, 3, 14.
Example: 2 * = 2 * 3, 14 = 6, 28
Step 3. Divide the angular frequency by twice the value of pi
Divide the angular frequency of the wave, in radians per second, by 6, 28, twice the value of pi.
Example: f = / (2π) = 7, 17 / (2 * 3, 14) = 7, 17 / 6, 28 = 1, 14
Step 4. Write down your answers
This last calculation will tell the frequency of the wave. Write your answer in Hertz, Hz, the unit of frequency.
