How to Calculate Frequency

Recipe. The formula for calculating wave frequency in a vacuum is similar to the formula for calculating the frequency in a non-vacuum environment. However, in a vacuum, the wave speed is not affected by other factors, so the speed of electromagnetic waves in this case is equal to the mathematical constant of the speed of light. Therefore, the calculation formula is: f = C /

• Where f is the frequency, C is the speed of light, and λ is the wavelength.
• For example, an electromagnetic wave has a wavelength of 573 nm when traveling in a vacuum. What is the frequency of this electromagnetic wave?

Convert wavelengths to meters if necessary. When the problem gives the wavelength in meters, we do not need to change. However, if the wavelength is given in another unit, such as a micrometer, you need to convert it to meters by dividing that value by the number of micrometers in a meter.

• Note that when the given values are very large or very small, we need to write those values in standard scientific notation. Here, values can be written in standard or non-standard form, but in assignments or tests as well as when participating in forums, you should write in standard scientific notation.
• Example: = 573 nm
  • 573 nm x (1 m / 10^9 nm) = 5.73 x 10^-7 m = 0.000000573

Divide the speed of light by the wavelength. ^[1] The speed of light is a constant, so in case the problem is given this value or not, we still use 3.00 x 10^8 m/s as the speed of light. Divide this value by the wavelength in meters.

• Example: f = C / = 3.00 x 10^8 / 5.73 x 10^-7 = 5.24 x 10^14

Record the answer. Calculating according to the steps above, we have the frequency value. When writing your answer, you need to include the units along with the value. The unit of frequency is Hertz, Hz .

• Example: The frequency of the wave is 5.24 x 10^14 Hz.

Recipe. Frequency and time required to complete a wave oscillation are two quantities that are inversely proportional to each other. Therefore, the formula for calculating the frequency when the time to complete the oscillation is known is: f = 1 / T ^[2]

• Where f is the frequency and T is the period time or amount of time required to complete one oscillation.
• Example A: A wave completes an oscillation in 0.32 seconds. What is the frequency of this wave?
• Example B: In 0.57 seconds, a wave completes 15 oscillations. What is the frequency of the wave?

Divide the number of oscillations by the total time. Usually, the problem will state the time it takes to complete an oscillation, in this case we take the reciprocal of the period time (take 1 divided by the period T ). If the period of time available is the period of multiple oscillations, you need to divide the number of oscillations by the total period of time it takes to complete all of them.

• Example A: f = 1 / T = 1 / 0.32 = 3.125
• Example B: f = 1 / T = 15 / 0.57 = 26.316

Record the answer. By doing the above calculation we will get the frequency of the wave. You need to include the frequency unit as Herzt, Hz .

• Example A: The frequency of the wave is 3.125 Hz.
• Example B: The frequency of the wave is 26.316 Hz.

Recipe. Once the angular frequency of a wave is known, to calculate the standard frequency of that wave, we apply the formula: f = / (2π) ^[3]

• where f is the reference frequency and ω is the corner frequency. As with other problems, π is the constant pi.
• For example, a wave moves in circular motion with an angular frequency of 7.16 radians per second. What is the frequency of the wave?

Double the pi value. To determine the denominator according to the above formula, we multiply the value of pi, or 3.14, by 2.

• Example: 2 * = 2 * 3.14 = 6.28

Divide the angular frequency by the product of pi and 2. Take the angular frequency of the wave, given in radians per second, and divide by 6.28, the value obtained by doubling the value of the constant pi.

• Example: f = / (2π) = 7.17 / (2 * 3.14) = 7.17 / 6.28 = 1.14