# What is the mathematical relationship between period and frequency of a wave

### Frequency and Period of a Wave

Jul 17, Like in waves how much time did a wave take to complete one vibration or oscillation. On the other hand frequency is the amount of cycles done in one second. Frequency, f, is how many cycles of an oscillation occur per second and is measured in cycles per second or hertz (Hz). The period of a wave, T, is the amount of. In mathematical terms, the frequency is the number of complete vibrational cycles of a medium per a given amount of time. The quantity frequency is often confused with the quantity period. Period refers to Do you observe the relationship?.

For example, it is not uncommon to hear a question like "How frequently do you mow the lawn during the summer months? If a coil of slinky makes 2 vibrational cycles in one second, then the frequency is 2 Hz.

If a coil of slinky makes 3 vibrational cycles in one second, then the frequency is 3 Hz. The quantity frequency is often confused with the quantity period. Period refers to the time that it takes to do something. When an event occurs repeatedly, then we say that the event is periodic and refer to the time for the event to repeat itself as the period. The period of a wave is the time for a particle on a medium to make one complete vibrational cycle.

### What is the relationship between frequency and period? - The Handy Physics Answer Book

Period, being a time, is measured in units of time such as seconds, hours, days or years. The period of orbit for the Earth around the Sun is approximately days; it takes days for the Earth to complete a cycle. The period of a typical class at a high school might be 55 minutes; every 55 minutes a class cycle begins 50 minutes for class and 5 minutes for passing time means that a class begins every 55 minutes.

The period for the minute hand on a clock is seconds 60 minutes ; it takes the minute hand seconds to complete one cycle around the clock. Frequency and period are distinctly different, yet related, quantities.

Frequency refers to how often something happens.

## Frequency and Period of a Wave

Period refers to the time it takes something to happen. Frequency is a rate quantity. In mathematical terms, both the quantities are reciprocal of each other. In equation form, frequency and period are expressed as: It can also be expressed as: The frequency and period are inversely proportional to each other. Because only one cycle occurs in a second, frequency of the wave would be 1 cycle per second. And if the wave took half a second to oscillate the complete cycle, the period of that wave would be 0.

So, longer the time period, lower the frequency and vice-versa. Comparison Chart Summary of Period Vs. Frequency Both frequency and time period are the fundamental parameters of waves, related to each other, yet they are distinctly different in terms of quantity. The frequency of a wave is related to rate quantity, whereas the time period of a wave is related to time quantity. The time period refers to the time it takes for a wave to complete one full cycle of oscillation or vibration, which is inverse of the frequency.

The frequency refers to the number of vibrations that occur in one second, which is the inverse of time period. Frequency is usually measured in Hertz Hz and period is measured in seconds.

Both are inversely proportional to each other, which means if the frequency is higher, then the period is lower, and vice-versa. If you like this article or our site.

The speed of light has been given the letter c. In fact, as with all mathematical letters it is just a label and any letter would do providing we state what we mean when we use it.

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Another way of writing this is: This means a three with eight zeros behind it, i. Again this is just a label, or shorthand, in order to allow us to work quickly with the equation. Wavelengths are usually measured in metres.

Providing we know any two of the three quantities we can find the other one, either directly or by rearranging the equation. The next section solves the equation as it is, and there is a calculator for frequency, wavelength and speed here. Solving the Equation In this example we will consider the frequency of radio waves. Radio waves are just another form of "light", i. Let's say we have a radio with a dial that is only marked in MHz.