How to Calculate Frequency

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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.

Equations for Finding Frequency

When you have a wavelength (λ) and a velocity (V), find frequency by using the equation f = V / λ, or f = C / λ for electromagnetic waves. If you’re calculating frequency given a time (T), use f = 1/T. Use f = ω / (2π) if you’re given an angular frequency (ω).

Method 1
Method 1 of 4:

Frequency from Wavelength

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  1. The formula for frequency, when given wavelength and the velocity of the wave, is written as: f = V / λ [1]
    • 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?
  2. 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]
    • 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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  3. Divide the velocity of the wave, V , by the wavelength converted into meters, λ , in order to find the frequency, f . [3]
    • Example: f = V / λ = 320 / 0.000000322 = 993788819.88 = 9.94 x 10^8
  4. 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

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  1. 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]
    • 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?
  2. 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
  3. 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]
    • Example: f = C / λ = 3.00 x 10^8 / 5.73 x 10^-7 = 5.24 x 10^14
  4. 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

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  1. 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?
  2. 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]
    • Example A: f = 1 / T = 1 / 0.32 = 3.125
    • Example B: f = 1 / T = 15 / 0.57 = 26.316
  3. 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

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  1. 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]
    • 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?
  2. 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
  3. Divide the angular frequency of the wave, given in radians per second, by 6.28, the doubled value of pi. [8]
    • Example: f = ω / (2π) = 7.17 / (2 * 3.14) = 7.17 / 6.28 = 1.14
  4. 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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Expert Q&A

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  • Question
    How can I easily practice calculating Frequency for my exams?
    Kevin Wang
    Math Tutor
    Kevin Wang is a Math Tutor based in New York, New York. Kevin has been tutoring math for over 10 years, and specializes in K-12 math topics and standardized tests, such as SAT and ACT. Kevin has an economics background and a career in both finance and marketing analytics. His interest in tutoring goes back even longer than his career. He discovered tutoring at the start of his university career and enjoys it as a way to stay sharp with fundamental skills and remain up to date with trends in our education system. Kevin received a BS in Economics from Duke University.
    Kevin Wang
    Math Tutor
    Expert Answer
    When studying for frequency calculations for your upcoming exams, knowing exactly where you need to study is important. After you have practiced your test questions, you will start to notice a pattern in problems that you consistently get wrong. Whether it be graph interpretation, word problems, or solving for the unknown in reverse, knowing these areas is what's going to make you more accurate and swift. Of course, some review of basic math is necessary, but knowing what kinds of questions you will face can also be very helpful. Consistent practice and post-practice analysis will allow you to build a better study strategy and become more confident when performing the frequency calculations.
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  • Question
    What is the frequency if 80 oscillations are completed in 1 second?
    Community Answer
    Frequency is the number of oscillations completed in a second. The answer would be 80 Hertz.
    Thanks! We're glad this was helpful.
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  • Question
    Do atoms have a frequency and, if so, does it mean everything vibrates?
    Donagan
    Top Answerer
    Atoms have energy. Energy is often characterized as vibration. Vibration possesses frequency. So, yes, everything could be thought of as vibrating at the atomic level.
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      References

      1. ↑ https://www.youtube.com/watch?v=LgYMxH1LCdo
      2. ↑ https://www.youtube.com/watch?v=LgYMxH1LCdo
      3. ↑ https://www.youtube.com/watch?v=LgYMxH1LCdo
      4. ↑ https://www.cuemath.com/frequency-formula/
      5. ↑ https://www.cuemath.com/frequency-formula/
      6. ↑ https://www.cuemath.com/frequency-formula/
      7. ↑ https://sciencing.com/calculate-angular-frequency-6929625.html
      8. ↑ https://sciencing.com/calculate-angular-frequency-6929625.html

      About This Article

      Article Summary X

      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!

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