# What is the mathematical relationship between period and frequency

### BBC Bitesize - GCSE Physics (Single Science) - Properties of waves - AQA - Revision 2

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?. the period (T) is measured in seconds (s); frequency (f) is measured in hertz (Hz). Example. Calculate the time period of a wave with a frequency of 50 Hz. Wavelength, Period and Frequency The reason we have to be aware of this relationship is that our ears are sensitive to frequency, which we perceive as pitch.

Virtually every system oscillates or vibrates freely in a large variety of ways.

What do an ocean buoy, a guitar, a child in a swing, or the beating of heart all have in common? They all oscillate — meaning they move back and forth between two points. The human body itself is a treasure-trove of vibratory phenomena. Even the atoms in our body vibrate. Every system that oscillates has something in common. It involves force and energy. You start a motion by pushing the child in a swing or you can increase the energy of atoms vibrating in a crystal with heat.

So oscillations create waves. What do oscillations or waves have in common?

The feature that relates such phenomena is periodicity. A periodic motion is a motion that repeats itself over and over again at regular intervals, such as the one exhibited by a guitar string or the back and forth motion of a child in a swing. The time to complete one vibration cycle or oscillation is called the period of a wave. Frequency simply refers to the number of cycles of an oscillation occur per second.

Frequency of a wave simply refers to the number of complete cycles or oscillations that occur in one second. It is measured in cycles per second or hertz Hz. A cycle is one complete oscillation and a vibration can be a single or multiple events, whereas oscillations are mostly repetitive for a number of cycles.

Period is the inverse of frequency and is defined as the time taken for one complete round trip of the vibration or oscillation. It simply refers to the time for something to occur periodically and it is measured in seconds per cycle.

The time period is reciprocal of the frequency which means both the quantities are inversely proportional to each other. In equation form, period is expressed as: Difference between Period and Frequency Definition of Period and Frequency Both the terms period and frequency are related because they exhibit a certain pattern of movement, yet they are distinctly different.

Both are related to periodic phenomenon and are often confused with each other. 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. Period, being a time, is measured in units of time such as seconds, hours, days or years.

## Frequency and Period of a Wave

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.

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

Frequency refers to how often something happens. Period refers to the time it takes something to happen. Frequency is a rate quantity. Period is a time quantity. As an example of the distinction and the relatedness of frequency and period, consider a woodpecker that drums upon a tree at a periodic rate.

If the woodpecker drums upon a tree 2 times in one second, then the frequency is 2 Hz. Each drum must endure for one-half a second, so the period is 0.

If the woodpecker drums upon a tree 4 times in one second, then the frequency is 4 Hz; each drum must endure for one-fourth a second, so the period is 0. If the woodpecker drums upon a tree 5 times in one second, then the frequency is 5 Hz; each drum must endure for one-fifth a second, so the period is 0. Do you observe the relationship? Mathematically, the period is the reciprocal of the frequency and vice versa. In equation form, this is expressed as follows. Since the symbol f is used for frequency and the symbol T is used for period, these equations are also expressed as: The quantity frequency is also confused with the quantity speed.

The speed of an object refers to how fast an object is moving and is usually expressed as the distance traveled per time of travel.

**4. One Dimensional Waves - Relationship between the frequency, period and wavelength of a wave**

For a wave, the speed is the distance traveled by a given point on the wave such as a crest in a given period of time.