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Frequency, also called wave frequency, is a measurement of the total number of vibrations or oscillations made within a certain amount of time. There are a few different ways to calculate frequency based on the information you have available to you. Keep reading to learn some of the most common and useful versions.
Steps
Method 1
Method 1 of 4:Frequency from Wavelength

1Learn the formula. The formula for frequency, when given wavelength and the velocity of the wave, is written as: f = V / λ^{[1] X Research source }
 In this formula, f represents frequency, V represents the velocity of the wave, and λ represents the wavelength of the wave.
 Example: A certain sound wave traveling in the air has a wavelength of 322 nm when the velocity of sound is 320 m/s. What is the frequency of this sound wave?

2Convert the wavelength into meters, if necessary. If the wavelength is given in nanometers, you need to convert this value into meters by dividing it by the number of nanometers in a single meter.^{[2] X Research source }
 Note that when working with extremely small numbers or extremely large numbers, it is generally easier to write the values in scientific notation. The values will be shown in and out of their scientific notation forms for this example, but when writing your answer for homework, other schoolwork, or other formal forums, you should stick with scientific notation.
 Example: λ = 322 nm
 322 nm x (1 m / 10^9 nm) = 3.22 x 10^7 m = 0.000000322 m
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3Divide the velocity by the wavelength. Divide the velocity of the wave, V, by the wavelength converted into meters, λ, in order to find the frequency, f.^{[3] X Research source }
 Example: f = V / λ = 320 / 0.000000322 = 993788819.88 = 9.94 x 10^8

4Write your answer. After completing the previous step, you will have completed your calculation for the frequency of the wave. Write your answer in Hertz, Hz, which is the unit for frequency.
 Example: The frequency of this wave is 9.94 x 10^8 Hz.
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Method 2
Method 2 of 4:Frequency of Electromagnetic Waves in a Vacuum

1Learn the formula. The formula for the frequency of a wave in a vacuum is almost identical to that of a wave not in a vacuum. Since there are no outside influences on the velocity of the wave, though, you would use the mathematical constant for the speed of light, which electromagnetic waves would travel at under these conditions. As such, the formula is written as: f = C / λ^{[4] X Research source }
 In this formula, f represents frequency, C represents the velocity or speed of light, and λ represents the wavelength of the wave.
 Example: A particular wave of electromagnetic radiation has a wavelength of 573 nm when passing through a vacuum. What is the frequency of this electromagnetic wave?

2Convert the wavelength into meters, if necessary. When the problem gives you the wavelength in meters, no further action is needed. If, however, the wavelength is given in micrometers, you need to convert this value into meters by dividing it by the number of micrometers in a single meter.
 Note that when working with extremely small numbers or extremely large numbers, it is generally easier to write the values in scientific notation. The values will be shown in and out of their scientific notation forms for this example, but when writing your answer for homework, other schoolwork, or other formal forums, you should stick with scientific notation.
 Example: λ = 573 nm
 573 nm x (1 m / 10^9 nm) = 5.73 x 10^7 m = 0.000000573

3Divide the speed of light by the wavelength. The speed of light is a constant, so even if the problem does not provide you with a value, the value remains 3.00 x 10^8 m/s. Divide this value by the wavelength converted into meters.^{[5] X Research source }
 Example: f = C / λ = 3.00 x 10^8 / 5.73 x 10^7 = 5.24 x 10^14

4Write your answer. With this, you should have calculated the value of the frequency of the wave. Write your answer in Hertz, Hz, the unit for frequency.
 Example: The frequency of this wave is 5.24 x 10^14 Hz.
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Method 3
Method 3 of 4:Frequency from Time or Period

1Learn the formula. Frequency and the time taken to finish a single wave oscillation are inversely proportional. As such, the formula for calculating frequency when given the time taken to complete a wave cycle is written as: f = 1 / T
 In this formula, f represents frequency and T represents the time period or amount of time required to complete a single wave oscillation.
 Example A: The time for a certain wave to complete a single oscillation is 0.32 seconds. What is the frequency of this wave?
 Example B: In 0.57 seconds, a certain wave can complete 15 oscillations. What is the frequency of this wave?

2Divide the number of oscillations by the time period. Usually, you will be told how long it takes to complete a single oscillation, in which case, you would just divide the number 1 by the time period, T. If given a time period for numerous oscillations, however, you will need to divide the number of oscillations by the overall time period required to complete them.^{[6] X Research source }
 Example A: f = 1 / T = 1 / 0.32 = 3.125
 Example B: f = 1 / T = 15 / 0.57 = 26.316

3Write your answer. This calculation should tell you the frequency of the wave. Write your answer in Hertz, Hz, the unit for frequency.
 Example A: The frequency of this wave is 3.125 Hz.
 Example B: The frequency of this wave is 26.316 Hz.
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Method 4
Method 4 of 4:Frequency from Angular Frequency

1Learn the formula. When told the angular frequency of a wave but not the standard frequency of that same wave, the formula to calculate the standard frequency is written as: f = ω / (2π)^{[7] X Research source }
 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?

2Multiply pi by two. In order to find the denominator of the equation, you need to double the value of pi, 3.14.
 Example: 2 * π = 2 * 3.14 = 6.28

3Divide the angular frequency by the double of pi. Divide the angular frequency of the wave, given in radians per second, by 6.28, the doubled value of pi.^{[8] X Research source }
 Example: f = ω / (2π) = 7.17 / (2 * 3.14) = 7.17 / 6.28 = 1.14

4Write your answer. This final bit of calculation should indicate what the frequency of the wave is. Write your answer in Hertz, Hz, the unit for frequency.
 Example: The frequency of this wave is 1.14 Hz.
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Community Q&A

QuestionWhat is the frequency if 80 oscillations are completed in 1 second?Community AnswerFrequency is the number of oscillations completed in a second. The answer would be 80 Hertz.

QuestionDo atoms have a frequency and, if so, does it mean everything vibrates?DonaganTop AnswererAtoms have energy. Energy is often characterized as vibration. Vibration possesses frequency. So, yes, everything could be thought of as vibrating at the atomic level.

QuestionWhat's the definition of frequency?Community AnswerThe rate at which a vibration occurs that constitutes a wave, either in a material (as in sound waves), or in an electromagnetic field (as in radio waves and light), usually measured per second. The rate at which something occurs or is repeated over a particular period of time or in a given sample.

QuestionHow do I find frequency with time?Community AnswerYou can use the formula f = 1/T where T is the time period, f is the frequency.

QuestionWhat is the proper definition of angular frequency?DonaganTop AnswererIt is the number of rotations or oscillations in a unit of time. It is typically measured in degrees (or radians) per second.

QuestionHow do I calculate the frequency of the wave length 600nm?Community AnswerUse the formula c=λv. (c is the speed of light, or 2.998 x 10^8 m/s ; λ is the wavelength, or 600 nm from the given information ; and v is the frequency, the variable we are trying to find). Now it's just algebra. 2.998 x 10^8 m/s = 600 nm (v). You divide by 600 nm on both sides, of course first paying attention to units and converting 600 nm into 6 x 10^7 m. The answer ends up being (5 x 10^14) Hz. One Hz is equal to 1/s.

QuestionHow do I find the frequency of wave lengths?DonaganTop AnswererFind the frequency of an electromagnetic wave by dividing its wavelength into the speed of light.

QuestionHow do I calculate energy when the energy of a photon is not given?Community AnswerTo figure out the energy, use the E = hf equation. The energy of each photon is equal to Planck's constant, multiplied by the frequency of the light, h is always 6.63 * 10^34 Joule seconds, and the frequency is 6 * 10^14 Hz. Plug those in and solve, and you get 4 * 10^19 Joules.
Tips
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References
 ↑ https://www.youtube.com/watch?v=DOKPH5yLl_0
 ↑ https://www.youtube.com/watch?v=DOKPH5yLl_0
 ↑ https://www.youtube.com/watch?v=DOKPH5yLl_0
 ↑ http://hubblesite.org/reference_desk/faq/answer.php.id=72&cat=light
 ↑ http://hubblesite.org/reference_desk/faq/answer.php.id=72&cat=light
 ↑ http://www.sengpielaudio.com/calculatorperiod.htm
 ↑ http://www.sengpielaudio.com/calculatorperiod.htm
 ↑ http://mriquestions.com/angularfrequencyomega.html
About This Article
To calculate the frequency of a wave, divide the velocity of the wave by the wavelength. Write your answer in Hertz, or Hz, which is the unit for frequency. If you need to calculate the frequency from the time it takes to complete a wave cycle, or T, the frequency will be the inverse of the time, or 1 divided by T. Display this answer in Hertz as well. Keep reading to learn how to calculate frequency from angular frequency!