Frequency of a wave

The frequency of a wave is the number of vibrations in a given time. The unit of time that we use to see how often a particle vibrates is the second. If a particle vibrates 100 times every second, the frequency is 100 vibrations or 100 cycles per second.

Unit of frequency

The unit of frequency is the Hertz and the symbol is Hz. It is named after Heinrich Rudolf Hertz who demonstrated radio waves in 1886.

1 cycle per second is equal to 1 Hertz.

5 cycles per second is 5 Hertz

For higher frequency, the kilohertz, the megahertz, or the gigahertz are used.

1 kilohertz  = 1000 Hertz = 1000 cycles per second.

The frequency of AM radio waves is measured in kilohertz.

If the frequency at a specific station is 15 kilohertz, this means that the electrons in the antenna of the radio station are forced to vibrate 15000 times every second.

1 megahertz = 1 million Hertz = 1000000 Hertz = 1000000 cycles per second. 

The frequency of FM radio is measured in megahertz.

1 gigahertz = 1 billion Hertz = 1000000000 Hertz = 1000000000 cycles per second.

The frequency of a radar or a microwave is measured in gigahertz.

Frequency of a wave and the period

The period of a wave is the time it takes to complete just 1 vibration or 1 cycle.

If the frequency of a wave is 5 Hertz, we know that this means 5 cycles every second.

If 5 cycles are completed every second, then 1 cycle is completed every 1/5 second. The period is 1/5.

Generally speaking, the period is the inverse of the frequency.

Period  =  1 / frequency

By the same token, the frequency is the inverse of the period.

Frequency = 1 / period

Below, we show you a frequency of 1 cycle every 2 second.

Notice that 1 cycle is when you start at a maximum displacement of 10 cm and then reaches that maximum displacement of 10 cm again.

In other words, it takes 2 second to see another crest.

For a pendulum, the first crest on the left is the maximum displacement you pull it before releasing it. Then, it will take 2 seconds to go back to that same maximum displacement.

The frequency of the wave above is 0.5 Hertz or 0.5 cycle every second.

The period is the time it takes to complete 1 cycle. It takes 2 seconds to complete a cycle,  so the period is equal to 2 seconds.

You could also use the formula period = 1 / frequency

period = 1 / 0.5 = 2.