Frequency, also called wave frequency, is a quantity that measures the total number of repeated waves or oscillations in a given time interval. There are several ways to calculate the frequency, depending on the information and data available to you. Read on to learn some of the more common and useful ways.
Steps
Method 1 of 4: Method One: Calculating the Frequency from Wavelength
Step 1. Learn the formula
When the wavelength and speed of propagation are available, the formula for determining the frequency is written as follows: f = V / λ
- In this formula, f represents the frequency, V represents the propagation speed, and λ represents the wavelength.
- Example: a certain sound wave that propagates in the air has a wavelength of 322 nm, when the speed of sound is equal to 320 m / s. What is the frequency of the sound wave?
Step 2. If necessary, convert the wavelength to meters
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 single meter.
- Note that when working with extremely small or extremely large numbers, it is usually easier to write the values using the corresponding scientific symbols. For this example the values will be shown in both forms, symbolic and non-symbolic, but when writing your answer for homework, in class assignments or in related forums, you should always use the corresponding scientific symbols.
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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 speed by the wavelength
To find the frequency, f, divide the wave propagation speed, V, making sure that the wavelength is converted into meters, λ.
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 completed your calculation for the wave frequency. Write your response in Hertz, Hz, the unit of measurement for frequency.
Example: The wave velocity is 9.44 x 10 ^ 8 Hz
Method 2 of 4: Method Two: Calculating the Frequency of Electromagnetic Waves in Vacuum
Step 1. Learn the formula
The formula for calculating the frequency of the wave in vacuum is almost identical to that used to calculate the frequency of a standard wave. However, since the speed of the wave is not affected by external factors, it is necessary to use the mathematical constant of the speed of light, the speed at which, under these conditions, electromagnetic waves travel. Therefore, the formula is written as follows: f = C / λ
- In this formula, f represents the frequency, C represents the speed of light, and λ represents the wavelength.
- Example: a particular wave of electromagnetic radiation that propagates through the vacuum has a wavelength equal to 573 nm. What is the frequency of the electromagnetic wave?
Step 2. If necessary, convert the wavelength to meters
When the problem gives you the wavelength in meters, no action is required. If, however, the wavelength is given in micrometers, it will be necessary to convert this value to meters by dividing it by the number of micrometers in one meter.
- Note that when working with extremely small or extremely large numbers, it is usually easier to write the values using the corresponding scientific symbols. For this example the values will be shown in both forms, symbolic and non-symbolic, but when writing your answer for homework, in class assignments or in related forums, you should always use the corresponding scientific symbols.
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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 is always 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
This way you will have converted the frequency value of the wave. Write your response in Hertz, Hz, the unit of measurement for frequency.
Example: the frequency of the wave is equal to 5, 24 x 10 ^ 14 Hz
Method 3 of 4: Method Three: Calculating Frequency From Time Interval
Step 1. Learn the formula
The frequency and time taken to complete a single wave oscillation are inversely proportional. Therefore, the formula used to calculate the frequency, having available the time taken to complete a wave cycle, is written as follows: f = 1 / T
- In this formula, f represents the frequency and T the period or time interval required to complete a single wave oscillation.
- Example A: The time it takes for a given wave to complete a single swing is 0.32 seconds. What is the frequency of the wave?
- Example B: A given wave can complete 15 swings in 0.57 seconds. What is the frequency of the wave?
Step 2. Divide the number of swings by the time interval
Usually you will be given the time it took to complete a single swing, in which case you will simply have to divide the number
Step 1. for the time interval, T.. However, if you are given the time span for several swings, you will need to divide the number of swings by the total time span 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 give you the frequency of the wave. Write your response in Hertz, Hz, the unit of measurement for frequency.
- Example A: The wave frequency is 3.15 Hz.
- Example B: The frequency of the wave is equal to 26, 316 Hz.
Method 4 of 4: Method Four: Calculate Frequency From Angular Frequency
Step 1. Learn the formula
If you have the angular frequency of a wave but not its standard frequency, the formula for determining the standard frequency is written as follows: f = ω / (2π)
- In this formula, f represents the frequency of the wave and ω represents the angular frequency. As with any other mathematical problem, π stands for pi, a mathematical constant.
- Example: a given wave rotates with an angular frequency of 7.17 radians per second. What is the frequency of the wave?
Step 2. Multiply π by two
To find the denominator of the equation it is necessary to double the value of π, 3, 14.
Example: 2 * π = 2 * 3, 14 = 6, 28
Step 3. Divide the angular frequency by twice π
With radians per second available, divide the angular frequency of the wave by 6.28, double the value of π.
Example: f = ω / (2π) = 7, 17 / (2 * 3, 14) = 7, 17/6, 28 = 1, 14
Step 4. Write your answer
The final part of this calculation should indicate the frequency of the wave. Write your response in Hertz, Hz, the unit of measurement for frequency.
