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# Graphical Representation of Sound Wave

Aug 22, 2022

## 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.

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

Time period = 0.001 s

The frequency is given by, ν = 1/T

Therefore, frequency = 1/0.001

frequency = 1000 Hz

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

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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