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# JEE Main Study Notes for Sound Waves: Basic Concepts, Tips and Sample Questions Sound Wave is one of the important topics from JEE Main exam point of view. Every year 1-2 questions are asked in the entrance examination. Some questions can be asked directly also. Basically, this topic relates to our daily life, hence it is very easy to understand. Inorder to score well in Physics, it is important for the candidates to score well by practicising previous years sample papers or question papers.

• The weightage of Sound Wave topics is not much high. This topics comprises of around 0-4% of the questions in JEE Main examination.
• The sub-topics that are included under Sound Wave are Speed of sound, Wave motion, types of wave motion, Laplace Correction, Sound Intensity, etc.

Read the article to know a study of sound waves, formulae, types of questions asked in the entrance examination and Tips and tricks to solve the questions.

### What is Sound wave?

Sound is a mechanical three dimensional and longitudinal wave that is created by a vibrating source such as the human vocal cords, a guitar string, the prongs of a tuning fork or the diaphragm of a loudspeaker. Also it is a form of energy due to mechanical vibrations. Therefore, sound waves require a medium for its propagation sound cannot travel a medium for its propagation. Sound cannot travel in a vacuum. The sound waves are propagated as longitudinal mechanical waves through solids, liquids and gases.

#### Properties of Sound Wave

It is the form of energy which produces, in us, the sensation of hearing. There are various properties of sound waves which are mentioned below:

• Sound Wave is Longitudinal in nature.

• It requires a material medium for its propagation

• Sound waves can be reflected

• The Sound waves suffer refraction

• It shows the phenomenon of interference

• Sound waves shows diffraction

• Sound propagates with a velocity much smaller than that of a light

• Sound gets absorbed in the medium through which it passes

### What is Wave Motion?

Wave motion is a type of motion in which the disturbance travels from one point of the medium to another but the particles of the medium do not travel from one point to another. The wave basically carries the energy being transferred from one particle to the another/neighbouring particle. For the propagation of waves, the medium must have inertia and elasticity. Because of the vibration of the particles at their own position caused externally or internally, the disturbance (Wave) is transferred from particle to particle.

#### Types of Wave Motion

There are two types of Wave Motion that are given below:

1. Mechanical Waves: The Mechanical waves require material medium for their propagation. For example- Waves in stretched string, Sound waves, etc. Under the mechanical waves it is further divided into two waves:

• Transverse Wave: The waves having the property where all the individual particles experience displacement perpendicular to the direction of the propagation of the wave. Transverse wave is generally a harmonic wave i.e. either the wave general has the sine or cosine shape. For example: Wave in a string, AC Current, etc.

In case of waves in a string, any point on the string vibrates up and down with no horizontal motion at all. An individual point on the string oscillates with some amplitude as a wave travels past.

• Longitudinal waves: The wave in which the particle experiences displacement parallel to the direction of the propagation. For example Sound waves, Spring motion. Incase of sound waves, the vibrations create a series of compression and expansion and the wave travels along the compression in the direction of the propagation.

2. Non- Mechanical Waves or electromagnetic waves: These waves do not require any material medium for their propagation. For example- x-rays, light waves, etc.

### Speed of Sound waves in Solid, Liquid, Gases

#### Newton’s Formula for speed

Newton showed that the speed of sound in a medium

Where, E= Modulus of elasticity of the medium

P= The density of the medium

#### Speed of Sound Waves in Solids

Where, Y= Young’s modulus of the solid

P= density of the solid medium

#### Speed of Sound Waves in Gases

Newton considered the propagation of sound waves through gases as an isothermal process PV= Constant (as the medium is into getting heated up when sound is passing through it) then he stated,

Where, P= Pressure of the Gas (Isothermal Bulk Modulus of gas) there was a huge discrepancy in the speed of sound determined by using this formula with the experimentally determined values. Hence a correction to this formula was given by Laplace, therefore it is known as Laplace Correction.

#### Speed of Sound Waves in Liquid

Where, B=Bulk Modulus of the liquid

P= Density of the Liquid

### Laplace Correction

According to Laplace, the propagation of sound waves in gas takes place adibatically. So the adiabatic bulk modulus of the gas (yP) has to be used. Hence the speed of sound waves in the gas will be:

Where, yP= Adiabatic Bulk Modulus of the gas

P= The density of the medium

#### Factors Affecting the Speed of Sound in Gases

The factors that affects the speed of sound in gases are:

• Effect of Temperature

• Effect of density of the gas

• Effect of pressure

• Effect of Humidity

• Effect of Wind

• Effect of amplitude

• Effect of change in frequency or wavelength of sound wave

### Intensity of Sound

Like any other progressive wave, sound waves also carry energy from one point to space to the other. The energy can be used to work, for example, Forcing the eardrums to vibrate or in the extreme case of a sonic boom created by a supersonic jet, can even cause glass panes of windows to crack. The amount of energy transmitted by a sinusoidal sound wave per unit time through each unit area perpendicular to the direction of sound propagation is called the intensity I and is given by-

Where, V is the speed of sound propagation

### Loudness

Audible Intensity range for Human Beings:

The ability of humans to perceive intensity at different frequencies is different. The perception of intensity is maximum at 1000 Hz and perception of intensity decreases as the frequency increases or decreases from 1000 Hz.

• The overall perception of intensity of sound to the human ear is known as Loudness.

• Decibel Scale is the logarithmic scale which is used for comparing two sound intensities.

• Human ears do not perceive loudness on a linear intensity scale rather it perceives loudness on logarithmic intensity scale.

For example: If Intensity is increased 10 times human ear does not perceive 10 times increase in loudness. It roughly perceived that loudness doubled where intensity increased by 10 times. Hence it is prudent to define a logarithmic scale of intensity.

#### Effect of Pressure

According to Boyle’s Law, If the Pressure is increased at a constant temperature than,

PV= Constant (For a fixed mass of gas)

P= Density of the gas (for the fixed value of density)

P/P = Constant

Therefore, change in pressure does not affect the speed of sound waves through a gas.

#### Effect of Temperature

Velocity of sound in a gas,

For perfect gas

PV= nRT (for 1 mole of gas)

#### Effect of Humidity:

With increase in humidity, density of air decreases. So with rise in humidity velocity of sound increases. This is why sound travels faster in humid air (rainy season) than in dry air (summer) at the same temperature.

#### Effect of wind velocity:

Because wind drifts the medium (air) along its direction of motion therefore the velocity of sound in a particular direction is the algebric sum of the velocity of sound and the component of wind velocity in that direction.

V resultant = V = Vw

Vw- Wind Speed

#### Effect of Amplitude:

From velocity relation

( for some amplitudes)

Generally the small amplitude does not affect the speed of sound in the gas. However, a very larger amplitude may affect the speed of the sound wave.

### Reflection of Waves

A mechanical wave is refracted and reflected at a boundary separating two media according to the usual laws of refraction anf reflection. When a sound wave is reflected from a rigid boundary or denser medium, the wave suffers phase reversal of pie but nature does not change i.e. on reflection the compression is reflected back as the compression and rarefaction as rarefaction. When a sound wave is reflected from an open boundary or rare medium, there is no phase change but the nature of the wave is changed i.e. on reflection, the rarefaction is reflected back as compression and compression as rarefaction.

#### Some Tips to Keep in mind

• For a wave, v=
• The Wave velocity of sound in air
• Particles velocity is given by . It changes with time. The wave velocity is the velocity with which disturbances travel in the medium and is given by
• In a tuning fork, the waves produced on the prongs are transverse whereas on the stem is longitudinal.
• When a wave reflects from a denser medium the phase change in pie and when the wave reflects from a rarer medium, the phase change is zero.
• A medium in which the speed of the wave is independent of the frequency of the waves is called non-dispersive. For example: The air is a non-dispersive medium for the sound waves.
• The Transverse waves can propagate in medium with shear modulus of elasticity. For example, solid whereas longitudinal waves need bulk modulus of elasticity hence can propagate in all medium solid, liquid and gas.

### What is Doppler Effect?

When a source of sound and an observer or both are in motion relative to each other there is an apparent change in frequency of sound as heard by the observer. This phenomenon is called the Doppler’s Effect.

1. When source is in motion and the observer at rest

(a) When source is moving towards observer

(b) When source is moving away from observer

Here, V= Velocity of sound

Vs= Velocity of source

V0= Source of frequency

2. When source is at rest and observer in the motion

V0= Velocity of observer

3. When source and observer both are in the motion

4. When the wind blows in the direction of sound- then in all the above formulae, V is replaced by V(V+W) where, W is the velocity of wind. If the wind blows in the opposite direction to sound then V is replaced by (V-W).

#### Few Tips to solve Doppler’s Questions

• The motion of the source of sound causes change in wavelength of the sound waves, which produces apparent change in frequency.
• The motion of the listener causes change in the number of waves received by the listener and this produces an apparent change in frequency.
• If a star goes away from the earth with velocity v, then the frequency of the light emitted from it changes from v to v`.

V` = v (1-v/c), where c is the velocity of light and where is called Doppler’s shift. If the wavelength of the observed waves decreases then the object from which the waves are coming is moving towards the listener and vice versa.

### Solved Sample Questions

Question: Is a sound wave with wavelength 1.32 cm and wave velocity 330 m/s audible to a human ear? Why?

Solution: Let us find the frequency v = . V is velocity of sound and is wavelength .

V = 330 / = 25000 Hz

Since the audible range of sound is 20 Hz to 20 kHz, this sound is not audiable. The frequency range is Ultrasonic sound frequency.

Question: A Motor car blowing a horn of frequency 124 vibration/sec moves with a velocity 72 km/hr towards a tall wall. The frequency of the reflected sound heard will be (velocity of sound in air is 330 m/s).

(A) 109 vibration/sec

(B) 132 vibration/sec

(C) 248 vibration/sec

(D) 140 vibration/sec

Solution: In the given condition source and listener are at the same position i.e. (car) for given condition, = 140 vibration/sec (D)

Question: A source and listener are both moving towards eachother with speed v/10 where v is the speed of sound. If the frequency of the note emitted by the source is f, the frequency heard by the listener would be

(A) 1.22 f

(B) f

(C) 1.27 f

(D) 1.11 f

Solution: (A) 1.22 f

Question: The frequency of sound wave is n and its velocity is v if the frequency is increased to 4n the velocity of the  wave will be

(A) 2v

(B) V

(C) v/4

(D) 4v

Solution: (B) v:  Wave velocity does not depend on the frequency. It depends upon the elasticity and intertia of the medium.

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