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# Frequency|Definition & Meaning

## Definition

**Frequency** is defined as the number of **incidents** of a **recurring** event occurring in a specific **time** interval. In **wave** propagation, it is defined as the number of **wave cycles** that pass through a point in one **second**. It defines the number of **oscillations** of a **periodic** signal that occur per **unit** second. It is denoted by “**f.**”

**Figure 1** shows two **waves** with different **frequencies**.

The **orange** wave has a higher** frequency** than the blue wave as more **repetitions** of a wave pattern are observed compared to the **blue** wave.

The **orange** wave **pattern** from point **P** to **Q** repeats **four** times in one second hence its frequency is **4 Hz**. Similarly, the wave pattern of the **blue** wave from point **A** to **B** recurs **two** times per **second**, therefore having a frequency of **2 Hz**.

The **wave** pattern from **A** to **B** and **P** to **Q** is known as the wave cycle. The greater the number of **wave cycles** passing in one second, the higher the **frequency**. A higher frequency increases the **speed** of wave propagation.

## Unit of Frequency

The frequency **unit** is named after Heinrich Rudolf Hertz, a German physicist of the nineteenth century. Its unit is “**Hertz**” abbreviated as “**Hz**” which is equal to one **cycle per second** (**/s**).

## Frequency of Periodic and Aperiodic Signals

A **periodic** signal repeats itself after a specific **interval** of time and has a **definite** shape. Whereas, an **aperiodic** signal does **not** recur at a **regular** time interval. It is also known as a **non-periodic** signal.

The **periodic** signal has a **single frequency** whereas an **aperiodic** signal has **multiple** frequencies spread over a continuous range.

## Frequency in Different Types of Mechanical Waves

A **mechanical** wave transfers **energy** through a medium by the **oscillation** of matter. There are **two** types of mechanical waves depending upon the **motion **of wave** particles**. The frequency of both **waves** is discussed below.

### Transverse Waves

The **particles** of a transverse wave move **perpendicularly** to the direction of **wave** propagation. **Examples** of transverse waves are **light** waves, **radio** waves and **water** waves formed when a stone is thrown into it.

The particles undergo a **to-and-fro** motion about their **mean** position. **Figure 2** shows a transverse wave.

The **maxima** and **minima** of the transverse are known as the **crest** and **trough** respectively. The wave from crest to crest or trough to trough makes a complete **wave cycle**. As a one-and-a-half wave cycle passes per **second** in the above figure, the frequency of the wave will be **1.5 Hz**.

### Longitudinal Waves

A **longitudinal** wave propagates **parallel** to the motion of the wave **particles.** An example of longitudinal waves is **sound** waves. **Figure 3** shows a longitudinal wave.

The wave **particles** of longitudinal waves have** back-and-forth** motion. It consists of compressions and **rarefactions** as shown in the figure. One **wave cycle** consists of one **compression** and one rarefaction.

The **frequency** of the periodic longitudinal wave is** 2 Hz** as two **wave cycles** pass through a point in one second.

#### Human Hearing Range of Frequency

**Human beings** can hear frequencies ranging from **20 Hz** to **20,000 Hz**. Infants can hear **higher** frequency sounds than **20 kHz** but lose this sensitivity to high frequency as they grow. **Adults** can listen to higher frequencies between the range of **15** to **17 kHz**.

## Frequency in Circular Motion

The **angular** or circular motion also has a frequency. One complete **rotation** forming a circle is equal to one** wave cycle**. So, the **frequency** in a circular motion can be defined as the number of **revolutions** per **second**.

## Important Relations of Frequency

The change in factors such as **wavelength** and **time period** changes the **frequency** of the periodic signal. The **mathematical** relation of the frequency with wavelength and time period is discussed below.

### Frequency and Wavelength

The **distance** between any two adjacent **troughs** or **crests** in a wave is called the wavelength. Alternatively, the distance of the wave to complete** one wave cycle** is also known as the **wavelength**. It is denoted by lambda(**λ**) and is measured in **meters(m)**.

The frequency and wavelength are **mathematically** related as follows:

c = fλ

The **product** of frequency **f** and wavelength** λ** gives the speed of light **c**. The speed of **light** is equal to 3 ✖ $10^8$ m/s. We can write the above equation as:

**f = c/λ**

It shows that increasing the **frequency** decreases the wavelength and vice versa. Hence, frequency and **wavelength** are **inversely** proportional.

**Figure 4** shows two waves with their frequency and wavelength.

The **blue** wave has a **greater wavelength** as compared to the **green** wave. So, the **frequency** of the **blue** wave(**0.75 Hz**) will be less than that of the **green** wave(**1.5 Hz**).

### Frequency and Time Period

The time taken by a **wave cycle** to pass from a fixed point is called the time **period**. The period** T** and the **frequency f** are mathematically related as follows:

**f = 1/T**

Both are **reciprocals** of each other. It means that **period** and **frequency** are **inversely** related to each other. The unit of **T** is **seconds**.

**Figure 5** shows the same waves as figure 4 for their **time periods** and** frequencies**.

The **green** wave with a higher **frequency** has a less **period** (**0.67 sec**) whereas the lower frequency **blue** wave has a greater period(**1.33 sec**).

## Examples of Frequency Related Problems

### Example 1 – Frequency and Wavelength

Calculate the **frequency** of a wave if its wavelength is** 1000 meters**.

### Solution

From the **given** data,

λ = 1000 m

The **formula** for frequency **f** and wavelength **λ** is:

λ = c/f

It can also be written as:

**f = c/λ**

Here,

**c** = 300,000,000 m/s

Placing the **values** in the above equation gives:

f = 300,000,000 / 1000

f = 300,000 Hz

**f = 300 kHz**

So, the **frequency** of the wave with a wavelength of 1000 m is **300 kHz**.

### Example 2 – Frequency and Time Period

Calculate the **time period** of a periodic signal if its frequency is **70 Hz**.

### Solution

The **formula** for time period** T** and frequency** f** is given as:

**T = 1/f**

Putting the value of **f = 70 Hz**, the time period is:

T = 1/70

**T = 0.0143 sec**

So, the** time period** of a wave with a frequency of 70 Hz is **0.0143 sec**.

*All the images are created using Geogebra.*