Music and Math Project

Frequency: How often does something happen?

How can we describe how often something happens? Let's think of an example. At a train station, we might want to say how often a train arrives, for instance: five times per hour. This is the frequency. When we speak about the frequency, it is very important to mention the length of the time interval over which you are counting. In the example with the train, this was an hour. Of course, if trains would arrive five times per year, this would mean that trains arrive way less often! The frequency is the number of times something happens during a certain interval of time, divided by the length of the time interval. In a formula, \[ \text{frequency} = \frac{\text{number of times something happens in time interval}}{\text{length of time interval}}. \]

Repeating events

Perhaps the time between trains can vary a lot, but some events happen very regularly. The frequency is the reciprocal of the period, which is the time between repeating events. That is, if we use the letter \(T\) for the period, and \(f\) for the frequency, then \[ f = \frac{1}{T}. \] For example, if every quarter of an hour, a ferry leaves, the ferry will leave \[ \frac{1}{\frac{1}{4} \text{ hr}} = 4 \frac{1}{\text{hr}}, \] that is \(4\) times an hour.