What is sound?

A sound wave is a mechanical wave (or mechanical vibration) that transit through media such as gas (air), liquid (water), and solid (wood).

In simple words, the sound waves cause the vibrations of the particles present in the medium. These vibrations are detected by the nerves present in human or animal's ears. The loudness of sound waves is measured in decibel or dB.

Production of sound waves

Sound waves are generated by the vibration of particles present in the medium through which sound propagates.  The vibration is nothing but a cyclic forward and backward motion of particles about a central point. These types of motions are also called oscillations.

For example, in violin, the strings are used to produce the sound as the string is stretched, the string undergoes vibrations and produces sound waves.

Propagation of sound waves

The traveling of sound waves through a medium is known as the propagation of sound waves.

Sound is propagated by the continuous or regular forward and backward motion of particles in the media. When a body (or object) undergoes vibrations, the particles undergo oscillations, these oscillations cause oscillation of neighboring particles. Thus the sound wave is displaced from its initial position. Thus, the disturbance is carried out from the producer to the receiver.

Sound propagation is not possible without a medium (air), to sound waves to travel from one place to another a medium is required. Hence, sound cannot travel in a vacuum.

For example, in space astronauts can speak, whistle, or yell with their own spacesuit but the other astronaut cannot hear because in space there is no atmosphere to propagate sound waves.

Medium

The medium is a substance or matter through which a wave can propagate or transmit. The media is mandatory for the transmission of sound waves. The media can be a solid, liquid, or gas. The sound waves can’t travel in a vacuum or empty space. Waves that needs a media or medium (solid, liquid, or gas) to travel, is called a mechanical wave.

Waves

A wave is also called an oscillation (or disturbance) that travels through space or matter. The wave motions are used to transmit the energy from one place to another place, the energy may be in the form of sound, heat, or light.   

Types of waves

The waves can be classified into three types. They are:

• Transverse wave.
• Longitudinal wave.
• Electromagnetic wave.

Transverse wave

In a transverse wave, these wave particles are moved perpendicular to the directions of wave travels.

Example: Surface ripples on water.

Longitudinal wave

In a longitudinal wave, the wave particles are moved parallel to the directions of wave travels.

Example includes,

• Sound wave.
• Ultrasonic wave.

Compressions and rarefactions

As sound waves propagate through a medium, the particles at particular regions undergo compression this region has density. These compressions occur at a region of the wave called the crest.

In some regions the particles undergo rarefaction. As the particles undergo rarefaction the region undergoes expansion and they have low density. These rarefactions occur at a region called the trough. 

Characteristics of sound waves

Sound waves have the following properties or characteristics. They are:

• Amplitude.
• Wavelength.
• Time period.
• Frequency.
• Velocity.

Amplitude

Amplitude is a vital characteristic of sound waves. A maximum displacement between each particle from its original position is called amplitude.

When a sound wave travels through a medium, the particles present inside the medium get disturbed from their original position. The amplitude is a measure of the strength of a wave.

It is denoted by A.

The S.I unit of the amplitude is meter (m).

Wavelength

The distance between the two adjacent curst or troughs of a wave is known as wavelength or a minimum distance between a curst and trough in a sound wave called wavelength.

It is denoted by the Greek letter lambda (λ). The S.I unit of the wavelength is meter (m).

Frequency

The number of vibrations that occur in a second is known as a frequency or the number of cycles of wave generated in one second is called frequency.

It is denoted by f.

The S.I unit of the frequency is Hertz or Hz.

Example

Let us consider 10 completed sound wave oscillations are generated in one second so the frequency of the sound wave is 10Hz or 10 cycles per second.

Time period

The required time to finish one vibration is known as the time period.

It is denoted by T.

The S.I unit of time period is second (s).

Relationship between a time period and frequency

The time essential to provide one full wave is called the time period of the wave.

Let us consider the time period of the wave is T seconds.

In T second one wave is produced. i.e, T=1

Now in second, the number of waves generated will be =$\frac{1}{T}$

Here, the number of waves produced in 1 second is called frequency.

So,               

$f=\frac{1}{T}$         (in Hz)

Where,

 f is the frequency of the wave.

T is the time period of the wave.

Velocity

The intervals traveled by a wave in one second are called the speed of the wave or velocity of the wave.

It is denoted by v.

The S.I unit of the velocity is m/s or ms^-1.

Properties of sound

The sound waves mainly have two properties. They are,

• Loudness.
• Pitch.

Loudness

Loudness is one of the main properties of sound waves. It is used to describe the strength of sound waves. The loudness is measured by the sound energy a time essential to reach human or animal ears. It depends on the amplitude of the sound waves.

Loudness is measured by decibel or dB.

Pitch

The pitch is also one of the main properties of the sound wave. It is used to describe the quality of sound waves or the rate of vibration is called pitch. It is also related to the frequency of sound waves.

Classification of sound based on aubibility

The range of frequencies of sound waves can be classified based on audibility. The frequencies are classified as audible and non-audible frequencies.

Audible frequency

The audible frequency of a human being's ear is about 20 Hz to 20,000 Hz. i.e, humans can hear only in the range of frequency is about 20 Hz to 20,000 Hz and we can’t able to hear below 20 Hz and above 20,000 Hz. These audible sound waves are also called sonic waves.

Non-audible frequency

The frequency having less than 20 Hz is called infrasonic waves and the frequency having greater than 20,000Hz is called ultrasonic waves.

Uses of sound waves

Ultrasound waves

The ultrasound waves are widely used for industrial properties and medical properties. Due to the large frequency, it has very high energy and it can able to penetrate up to a large distance. These properties of ultrasound waves are widely used for many purposes.

Due to the ultrasonic waves, the dolphins can find fish and it also detects the shark to prevent their attack and also it is used for medical diagnosis, therapy, and surgical tools.

Eco-cardiography

The ultrasonic waves are used to reflect from the heart, due to the reflection of ultrasonic waves we can able to get a graphical representation of a heart movement or action.

Ultrasonography

The ultrasound waves are used to produce imaging of internal organs present in the body by using echo techniques.

Sonar

Sonar is the abbreviation of sound navigation and ranging. It is an instrument that is used to determine the distance or direction of a depth area like sea, hills, etc.

Formula

The frequency of the sound wave is,

$f=\frac{1}{T}$        

Context and Applications

This topic is one of the important applications in all forms of classical mechanics and it is significant for both undergraduate and postgraduate courses, especially for bachelors and masters in science (physics).

Practice Problems

Question 1: Which of the following correctly relates the frequency (f), wavelength (λ) and velocity (v) of sound waves?

 (a) $V=\frac{\lambda }{2f}$                     

(b) $f= \frac{\lambda }{v^2}$

(c) $v=f \lambda$                       

(d) $f=\lambda -v$

Answer: The correct option is c.

Explanation:

We know that frequency of a wave is $f=\frac{1}{T}$.

Where, $f$ is a frequency and T is a time period.

Here, $speed = \frac{dis\tan ce}{ time}$

The speed of the wave is determined by velocity v and the distance of a wave is determined by wavelength λ.

Substitute, $v= \frac{\lambda }{T}$

but,

$\frac{1}{T}= f$

$v= \lambda f$

Therefore,

$\nu =\lambda f$.

Question 2: Which of the following is not a characteristic of sound?

(a) Loudness            

(b) Speed

(c) Timbre                

(d) Pitch

Answer: The correct option is b.

Explanation: We know that there are three basic characteristics of sound. They are loudness, timbre, and pitch.

Question 3: The velocity of sound wave in air is _________ .

(a) 1430 m/sec                                

(b) 245 m/sec

(c) 343 m/sec                                 

(d) 1500 m/sec

Answer: The correct option is c.

Explanation: The velocity of sound waves in air at 0°C is 332 m/sec and the velocity of sound waves in air at 20°C is 343 m/sec.

Question 4: Sound waves are _______ .

(a) Longitudinal waves                          

(b) Latitudinal waves

(c) Longitudinal mechanical wave     

(d) None of the above

Answer: The correct option is a.

Explanation: The sound waves are longitudinal waves due to the compression and rarefactions of the air produce them. These air particles vibrate parallel to the direction of propagation.

Question 5: The pitch of the sound depends upon _________ .

(a) Amplitude                 

(b) Time period

(c) Frequency               

 (d) Wavelength

Answer: The correct option is c.

Explanation: The pitch of the sound waves depends on the frequency of the vibrating body.