physics sound and waves for jee main 2015 - part i

SOUNDWAVE MOTION

What is motion ?

Displacement of a particle or energy from one point to anther point is known as motion.

Types of Motion

Translational motion :-

the body moves along a straight line path or along a curved path.

e.g. motion of a train, car, crawling if insects etc.

Circular or Rotational motion

the body moves round and round along a circular path about an axis. e.g. motion of the blades of an electric fan, spinning top, merry-go-round etc.

Oscillatory or Vibrational motion :- the object moves to and fro, tracing the same path again and again in equal intervals of time.e.g. motion of a swing, needle of a sewing machine, prongs of a tuning fork etc.

Oscillator or Vibrator :- The particle performing oscillatory motion is called oscillator or vibrator.

Oscillation :- During oscillatory motion the oscillator performs number of same sets of vibration, in equal intervals of time One such set of vibration is called oscillation.

Periodic time or Period of oscillation :- The time taken by the particle to perform one oscillation is called period of oscillation (T).

It is measured in second.

Frequency of oscillation :- Number of oscillations performed by the particle in one second is called frequency of oscillation (n).

It is measured in hertz (Hz)

Amplitude of vibration :- The maximum displacement of the particle from its mean position is called amplitude (A) of its vibration. It is measured in metre.

Damped oscillations :- Generally when an object is set in to oscillations, it starts moving to and fro. During its motion it has to overcome the air resistance. For this, it has to spend energy. Thus, the energy of the particle goes on decreasing, which decreases its amplitude. So, after some time the object stops moving. Such oscillations are called damped oscillations.

Sustained Oscillations :- If energy is continuously supplied to the oscillator, the amplitude of oscillations remains constant. Such oscillations of constant amplitude are called sustained oscillations.

What is sound?

What is sound?

Energy or matter?Wave

Wave motion

The motion of the oscillatory disturbance through a medium is called wave motion.

Then What is wave ? Wave is defined as the oscillatory

disturbance travelling through a medium without change of form.

Wave motion is a doubly periodic phenomenon

When a wave travel through a medium, it is observed that at any given point of the medium, the form of the wave repeats from time to time, which shows that the wave is periodic in time.

Also at any instant of time, the form of waves repeats at equal distances, which shows that it is periodic in space.

Types of Waves

Waves

Mechanical

progressive Stationary

Electromagnetic

Mechanical waves :- The waves whichrequire material medium for theirpropagation are called mechanicalwaves. e.g. sound waves.

Non Mechanical waves :- The waveswhich does not require material mediumfor their propagation are calledmechanical waves. e.g. Light waves.

For successful propagation of mechanical wave the medium must possess following properties

1. The medium should be elastic

2. The medium should possess

3. The frictional resistance of the medium should be small

Progressive Waves

The waves which travel in the same direction continuously are called progressive waves.

Classification of Wave

progressive

Transverse Longitudinal

(I) Transverse waves :- The waves in which the particles of the medium vibrate in a direction

perpendicular to the direction of propagation of the wave are called transverse waves.

Characteristics of transverse waves are as follows

1. When the transverse waves travel through a medium the particles of the medium vibrate in a direction perpendicular to the direction of propagation of the waves.

2. The period and the amplitude of vibration of all the particles is same.

3. When a transverse wave travels through medium, the medium is divided in to alternate crests and troughs. The convex part of the wave is called crest and the concave part is called trough.

4. One crest and one trough forms wave. The distance between two consecutive crest or trough is called wavelength (λ) of the wave.

5. At every point in the medium the crests and the troughs are alternately produced and they follow each other as the wave propagates.

6. For the propagation of transverse waves the medium should possess elasticity of shape. transverse wave can pass only through solids and can not propagate through liquids or gases.

7. The velocity of transverse wave travelling through stretched string is given by

8. When transverse wave prorogate through the medium The pressure and density of medium will remain constant

T

vM

Sound is Longitudinal wave

The waves in which the particles of the medium vibrate in a direction parallel to the direction of propagation of the wave are called Longitudinal waves.

Longitudinal wave

Characteristics of longitudinal waves are as follows

1. When the longitudinal waves travel through a medium the particles of the medium vibrate in a direction parallel to the direction of propagation of the waves.

2. The period and the amplitude of vibration of all the particles is same.

3. When a longitudinal wave travels through medium, the medium is divided in to alternate compressions and rarefactions. The denser part of the wave is called compression and the rare part is called rarefaction.

4. One compression and one rarefaction forms one wave. The distance between two consecutive compressions or rarefactions is called wavelength (λ) of the wave.

5. At every point in the medium the rarefactions and the compressions are alternately produced and they follow each other as the wave propagates.

6. For the propagation of longitudinal waves the mediumshould possess elasticity of volume or bulk modulus, i.e. it should be able to regain its original volume after the waves have passed. All solids, liquids and gases possess elasticity of shape. So, longitudinal wave can pass through all of them.

M.C.Q. Q.1    The longitudinal wave travels in a medium along the

positive direction of X-axis, the particles of the medium vibrates

        (a.1) along Y- axis          (b.1) along X–axis            (c.1) along Z-axis           (d.1) along any direction

Q.2    The material medium required for the propagation of mechanical wave must posses

          (a.2) Elasticity                      (b.2) Inertia                    (c.2) Small frictional resistance   (d.2) All of these

Q.3    Longitudinal waves can’t travel through ________          (a.3) Solid                       (b.3) Liquid                  

   (c.3) Vacuum                  (d.3) Gas

Answers

   (b.1) along X–axis

(d.2) All of these

(c.3) Vacuum 

7. The velocity of longitudinal wave travelling through medium is given by

8. When transverse wave prorogate through the medium The pressure and density of medium will vary.

E

V

Velocity of wave In one oscillation, a wave travels a

distance of one wavelength (λ). For one

oscillation, it takes periodic time (T). Hence, velocity (v) of the wave is given as

distance λ velocity = ---------- = --- Time T but 1/T = frequency n of the wave

v = nλ

Newton’s formula for Velocity of sound

Newton’s an empirical formula for this velocity as :

Where E and ρ are the elasticity and density of the medium.

E

ForSolids V

For gaseous media, (isothermal) .

At N.T.P. P = 1.013 x 105 N/m2 and ρ= 1.293 kg/m3, v = 280m/s.

But, the practically observed value of speed of sound in air at N.T.P. is 331 m/s

28% less than the actual value.

P

V

Laplace’s Correction :-

According to Laplace, the volumetric changes, that are taking place during propagation of sound, are adiabatic and not isothermal. So, elasticity E should be replaced by γP instead of P, where γ is the ratio of molar specific heat capacity of the gas at constant pressure (CP) to its molar specific heat capacity at constant volume (CV). Thus,

For air the value of g is 1.4. Substituting this value for E, we get the speed of sound in air as 331m/s, which is in perfect agreement with the practical value. Hence, the above modification is called Laplace’s correction and the formula is called Laplace’s corrected formula for velocity of sound.

P

V

CPv where

C