(This article was translated from Japanese to English using DeepL.)

In this lecture, we will introduce some frequently used terms in the field of waves.

## Sinusoidal wave

In high school physics, we mostly deal with the simplest wave, called **sinusoidal wave**.

As you can see in the figure above, **the sinusoidal wave has alternating crest and trough and repeats the same shape.**

We will count the number of waves according to how many times this “set of crests and troughs” is repeated.

Let’s think specifically in terms of waves traveling down a rope.

Holding the end of the rope by hand and swinging it up and down produces a sinusoidal wave in the rope.

As the rope continues to swing, waves are created one after another.

Waves created in this way are called **continuous wave**.

On the other hand, those that stop swinging halfway through are called **pulse wave**.

We will also count the swing of the arm that creates one wave on the rope as one oscillation.

## Period

**The time it takes to vibrate a medium once is called the period.**

For example,

Slow swing of the rope → Long period,

Quick swing of the rope → Short period.

## Frequency

**The number of times a medium vibrates per second is called the frequency.**

For example,

Slow swing of the rope → Low frequency,

Quick swing of the rope → High frequency.

## Relation between period and frequency

Let’s reiterate what I wrote above.

Slow swing of the rope → Long period/Low frequency,

Quick swing of the rope → Short period/High frequency.

There seems to be some relationship between period and frequency.

So, let’s check the definition again.

**Period is T[s] → The medium oscillates once every T seconds.**

**Frequency is f[Hz] → The medium vibrates f times per second.**

Since the key points in both cases are the number of oscillations and the time of oscillation, let’s create a ratio of the number of oscillations to the time.

**Period is T[s] → Number of oscillations: time = 1 : T ,**

**Frequency is f[Hz] → Number of oscillations: time = f : 1 .**

Since both of these ratios represent the same ratio,

**1 ： T ＝ f ： 1**

From this equation, we see that the relationship ** fT = 1** holds between the period

*T*and the frequency

*f*.

This relation is used frequently, so please memorize it!

## Summary of this lecture

## Next Time

In the next lecture, we will do calculations related to waves.

https://www.yukimura-physics.com/entry/wave-f03