Wavelength, Frequency and Time Period of Sound Waves

Introduction

Sound travels through a medium as a wave. A sound wave consists of alternate compressions and rarefactions. To describe a sound wave clearly, we use some important quantities such as wavelength, frequency, and time period.

These quantities help us understand how sound waves are arranged, how often they repeat, and how fast the particles of the medium complete one oscillation.

Characteristics of a Sound Wave

The main characteristics used to describe a sound wave are:

  • Wavelength
  • Frequency
  • Time period
  • Amplitude
  • Speed

In this topic, we will study wavelength, frequency, and time period.

Wavelength

The distance between two consecutive crests or two consecutive troughs of a wave is called the wavelength.

In a sound wave, wavelength can also be understood as the distance between two consecutive compressions or two consecutive rarefactions.

Wavelength = Distance between two consecutive crests or troughs

Wavelength is usually represented by the Greek letter \(\lambda\) called lambda.

Symbol of wavelength = \(\lambda\)

SI Unit of Wavelength

Since wavelength is a distance, its SI unit is metre.

SI unit of wavelength = metre (m)

Figure

Wavelength of a Sound Wave Distance Density Average density Crest Crest Trough Trough
\(\lambda\)
Crest to crest distance
\(\lambda\)
Trough to trough distance Wavelength is the distance between two consecutive similar points.

Explanation of the Figure

The figure shows a graphical representation of a sound wave. The highest points are called crests and the lowest points are called troughs.

The distance between two consecutive crests is one wavelength. Similarly, the distance between two consecutive troughs is also one wavelength.

Long Wavelength and Short Wavelength

A sound wave may have a long wavelength or a short wavelength.

  • When the distance between consecutive crests or troughs is large, the wavelength is long.
  • When the distance between consecutive crests or troughs is small, the wavelength is short.

Frequency

Frequency of a sound wave is the number of complete density oscillations at a fixed point per unit time.

In simple words, frequency tells us how many complete oscillations occur in one second.

Frequency = Number of oscillations per unit time

Frequency is usually represented by the Greek letter \(\nu\) called nu.

Symbol of frequency = \(\nu\)

SI Unit of Frequency

The SI unit of frequency is per second or hertz.

The symbol of hertz is Hz.

SI unit of frequency = hertz (Hz)

If a sound wave completes 1 oscillation in 1 second, its frequency is 1 Hz.

One Complete Oscillation

In a sound wave, the density of the medium at a fixed point changes from maximum density to minimum density and then again to maximum density.

This complete change is called one complete oscillation.

Maximum density → Minimum density → Maximum density = One complete oscillation

Time Period

The time taken by a sound wave to complete one density oscillation at a fixed point is called the time period.

Time period = Time taken for one complete oscillation

Time period is represented by the symbol \(T\).

Symbol of time period = \(T\)

SI Unit of Time Period

Since time period is a time, its SI unit is second.

SI unit of time period = second (s)

Relation Between Frequency and Time Period

Frequency and time period are inversely related to each other.

If the time period is small, frequency is high. If the time period is large, frequency is low.

\(\nu=\frac{1}{T}\)

where,

  • \(\nu\) = Frequency of the wave
  • \(T\) = Time period of the wave

This relation shows that frequency is the reciprocal of time period.

Comparison Between Wavelength, Frequency and Time Period

Quantity Meaning Symbol SI Unit
Wavelength Distance between two consecutive crests or troughs \(\lambda\) metre (m)
Frequency Number of oscillations per unit time \(\nu\) hertz (Hz)
Time period Time taken for one complete oscillation \(T\) second (s)

Example 1

If there are 10 complete density oscillations in 2 seconds at a fixed point, find the frequency of the sound wave.

Given,

  • Number of oscillations = 10
  • Time taken = \(2\,s\)

Using,

\(\text{Frequency}=\frac{\text{Number of oscillations}}{\text{Time taken}}\)

\(\nu=\frac{10}{2}\)

\(\nu=5\,Hz\)

Therefore, the frequency of the sound wave is 5 Hz.

Example 2

If the frequency of a sound wave is \(5\,Hz\), find its time period.

Given,

  • Frequency, \(\nu = 5\,Hz\)

Using,

\(T=\frac{1}{\nu}\)

\(T=\frac{1}{5}\)

\(T=0.2\,s\)

Therefore, the time period of the sound wave is 0.2 s.

Frequency and Musical Notes

Different musical notes have different frequencies. This is why different notes sound different to our ears.

For example, the frequency generally increases as we move from lower musical notes to higher musical notes.

A tuning fork can produce a nearly single-frequency sound. Oral whistling can also produce a nearly single-frequency sound.

High Frequency and Low Frequency

Frequency tells us how frequently the oscillations repeat.

  • A high-frequency sound has more oscillations per second.
  • A low-frequency sound has fewer oscillations per second.

A shorter time period corresponds to a higher frequency, while a longer time period corresponds to a lower frequency.

Examples from Daily Life

  • A tuning fork produces a sound of nearly single frequency.
  • Different musical notes have different frequencies.
  • A whistle usually produces a high-frequency sound.
  • A drum usually produces a lower-frequency sound compared to a whistle.
  • A short wavelength wave has crests and troughs closer together.
  • A long wavelength wave has crests and troughs farther apart.

Important Terms

1. Wavelength

The distance between two consecutive crests or two consecutive troughs of a wave.

2. Frequency

The number of complete oscillations at a fixed point per unit time.

3. Time Period

The time taken for one complete oscillation at a fixed point.

4. Crest

The highest point of the graphical representation of a wave.

5. Trough

The lowest point of the graphical representation of a wave.

6. Oscillation

One complete periodic change of density from maximum to minimum and back to maximum.

Important Points

  • Wavelength, frequency, and time period are important characteristics of a sound wave.
  • Wavelength is the distance between two consecutive crests or troughs.
  • Wavelength is represented by \(\lambda\).
  • The SI unit of wavelength is metre (m).
  • Frequency is the number of oscillations per unit time.
  • Frequency is represented by \(\nu\).
  • The SI unit of frequency is hertz (Hz).
  • Time period is the time taken for one complete oscillation.
  • Time period is represented by \(T\).
  • The SI unit of time period is second (s).
  • Frequency and time period are inversely related.
  • The relation between frequency and time period is \(\nu=\frac{1}{T}\).

Conclusion

Wavelength, frequency, and time period are important quantities used to describe sound waves. Wavelength is the distance between two consecutive crests or troughs and is represented by \(\lambda\). Frequency is the number of complete oscillations per unit time and is represented by \(\nu\). Time period is the time taken for one complete oscillation and is represented by \(T\). Frequency and time period are inversely related by the relation \(\nu=\frac{1}{T}\).

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