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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.
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.
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.
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
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.
There are two types of Wave Motion that are given below:
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.
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.
Newton showed that the speed of sound in a medium
Where, E= Modulus of elasticity of the medium
P= The density of the medium
Where, Y= Young’s modulus of the solid
P= density of the solid medium
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.
Where, B=Bulk Modulus of the liquid
P= Density of the Liquid
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
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
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
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.
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.
Velocity of sound in a gas,
For perfect gas
PV= nRT (for 1 mole of gas)
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.
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
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.
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.
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.
(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).
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.
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
(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
Solution: (B) v: Wave velocity does not depend on the frequency. It depends upon the elasticity and intertia of the medium.