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## Key Concepts

- Graphical representation of sound wave
- Wavelength
- Frequency
- Oscillations
- Time period
- Relation between frequency and time period

**Introduction:**

Sound waves can be graphically represented by plotting the density or the pressure variation against the distance at a particular instant of time. The sound waves are characterized by various quantities such as wavelength, frequency, time-period etc., which are indicated via a graphical representation of the sound wave. We will be looking at these characteristics of sound wave in this section.

**Explanation:**

### Graphical Representation of Sound Wave:

The density and/or pressure variations can be plotted against distance at a particular instant of time. The graph below shows the way in which the density or pressure of the medium vary when a sound wave propagates through it.

Compressions are the regions of high pressure and density and is represented by the **upper** portions of the curve.

Rarefactions are the regions of low pressure and density and is represented by the **lower** portions of the curve. i.e., the valleys.

The **peaks** represent the regions of **maximum compression, **i.e., they represent the highest density and pressure.

The **bottom most points **of the valleys represent the regions of **minimum compression **or maximum rarefaction, i.e., they represent the lowest density and pressure.

A peak is called a **crest** and a valley is called a **trough** of a wave.

**Wavelength: **

The distance between any two consecutive compressions or rarefactions is called the **wavelength**. Wavelength of a wave is denoted by a Greek letter “**λ**” called **lambda**. The SI unit of measurement of wavelength is **meter (m)**.

**Frequency:**

**Frequency** refers to how frequently an event takes place. The frequency of beating a drum refers to the number of times the drum is beaten in a unit time. The frequency of getting sixes when dice are thrown refers to the number of times the sixes are obtained on throwing the dice.

The propagation of a sound wave is characterized by the motion of alternate compressions and rarefactions, i.e., crests and troughs. The number of compressions or rarefactions that cross a particular point in a unit time is called the **frequency** of the wave. The frequency of a wave is denoted by a Greek letter “**ν**”called “nu” and is measured in the SI unit of **Hertz (Hz)**.

**Oscillation:**

When a sound wave propagates through a medium the density of a medium oscillates between a maximum and a minimum value.

This change in density or pressure from its maximum value to its minimum value and again to its maximum value makes one complete **oscillation**.

The parts of a wave which can be referred to as one complete oscillation, are shown by red dashed box in each picture below. Any of these can be referred to as a complete oscillation.

**Time period:**

The time taken by a wave to complete one oscillation is called its time period.

In other words, the time taken by two consecutive compressions or rarefactions to cross a fixed point is called **time period**.

It is denoted by a letter ‘**T’** and is measured in the SI units of ‘**seconds.’**

**Relation between frequency and time period: **

The frequency and time period are related by the following formula.

**ν**** = 1/T**

This formula can be used to calculate frequency of a sound wave when its time period is given and vice versa.

### Questions and Answers:

**Calculate the frequency of a sound wave whose time period is 0.001 s.**

**Answer: **

Time period = 0.001 s

The frequency is given by, **ν**** = 1/T**

Therefore, frequency = 1/0.001

frequency = **1000 Hz**

**Calculate the time period of the sound wave whose frequency is 50 Hz.**

**Answer: **

Frequency = 50 Hz

The frequency is given by, **ν**** = 1/T**

Thus, the time period is given by, T = 1/ν

Therefore, time period = 1/50

**time period = 0.02 s**

## Summary:

- The propagation of sound waves can br graphically represented by plotting the pressure or the density variations against distance at a particular instant of time.
- The crests represent the region with maximum compression and the troughs represent the region of minimum compression.
- The distance between any two consecutive compressions or rarefactions is called the wavelength (X).
- The number of compressions or rarefactions that cross a particular point in a unit time is called the frequency (V) of the wave.
- The change in density or pressure from its maximum value to its minimum value and again to its maximum value makes one complete oscillation.
- The time taken by two consecutive compressions or rarefactions to cross a fixed point is called time period.
- The SI units of wavelength, frequency and time period are m, Hz and s respectively.
- The frequency and time period are related by the following formula. v=1/T

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