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MHT-CET : Physics Entrance Exam

MHT - CET : Physics - Wave Motion Page 1

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Wave motion is defined as the mode of transfer of energy through an elastic medium by repeated oscillations of the particles of the medium about their mean positions.

 

 

 

Wave Motion is Doubly Periodic

 

  • When waves are propagated through a medium, the form of the waves repeats after equal intervals of time - wave motion is periodic in time.
  • The form of the waves keeps repeating at equal distance - wave motion is periodic in space.

 

 

 

Terms Used in the Study of Wave Motion

 

Amplitude (A): The maximum displacement of a particle of the medium from its mean position.
SI Unit
- metre (m)

Period (T): The time taken for one complete oscillation by any particle of the medium.
SI Unit
- second (s)

Frequency (n): The number of waves passing across any point of the medium in
one second is called the frequency of the wave.
SI Unit
- Hertz (Hz).

 

Frequency, n =

1

T

 

 

Wavelength (l)

 

It is the distance between two adjacent particles in the path of the wave motion which are exactly in the same phase.

It is the distance between two consecutive crests (or troughs or condensations or rarefactions).
SI Unit
- metre (m)

 

 

 

Velocity (n):

 

The distance covered by the wave in one second.
SI Unit
- metre/second (m/s).

 

 

Relation between Velocity, Frequency and Wavelength

 

In a time of one period (T), the wave travels a distance equal to one wavelength (l).

Hence, velocity, n =  

Distance covered

=

l

 \ v

l

time

T

T

 

But, T =  

1

=

 , v = nl

n

 

 

 

Simple Harmonic Progressive Wave

 

  • A wave which travels with finite velocity without any change in its form is called a progressive wave.
  • If the particles of the medium perform simple harmonic motion about their mean positions when the wave travels through the medium, the wave is called a simple harmonic progressive wave.
  • The amplitude and period of SHM is the same for every particle.

 

 

Equation of a Simple Harmonic Progressive Wave

 

 

Consider a simple harmonic progressive wave travelling in the positive direction of the x-axis.

At t = 0, displacement y = 0

Hence, the equation of motion at any instant, for a vibrating particle such as O, is given by      
y = A sin wt,

where A
amplitude

w angular velocity

For another particle B, at a distance
x from O, the equation of the motion is given by,

y = A sin (wt - f), since it lags behind in phase.
f is the phase lag with O.

A path difference of
l corresponds to a phase difference of 2p.

\ A path difference of x corresponds to a phase difference of  

2px

l

\ f =  

2px

l

\ The equation of motion of particle B can be written as,

y = A sin

(

w t -

2px

)

l

Since, this equation is true for any particle, it is the equation of the wave.

Since, w =  

2p

T

y = A sin  

(

2pt

-

2px

)

T

l

 

\ y = A sin 2p 

(

t

-

x

)

T

l


A simple harmonic progressive wave travelling along the negative
x - axis is represented

 

by y = A sin 2p

(

t

+

x

)

T

l

 

 

 

Different Forms

 

Since n =  

1

,

T

 

y = A sin 2p 

(

nt

-

x

)

l

 

\ y = A sin 2p

(

t

-

x

)

nl


But
v = nl

\ y = A sin 2p

(

t

-

x

)

v

 

But n =  

v

l

 

\ y = A sin

2p

 (vt - x)

l

 

 

Longitudinal Waves and Transverse Waves

 

On the basis of the direction of vibration of particles and direction of propagation of waves, waves are classified into two categories:
 (i) Longitudinal waves
(ii) Transverse waves

  • Longitudinal waves are those in which the particles of the medium vibrate parallel to the direction of propagation of the waves.
  • Transverse waves are those in which the particles of the medium vibrate perpendicular to the direction of propagation of the waves.

 

 

Longitudinal Waves

Transverse Waves

 

Particles vibrate parallel to the direction of propagation.

Particles vibrate perpendicular to the direction of propagation.

 

Travel in the form of alternate compressions and rarefactions.

Travel in the form of crests and troughs.

 

It can be propagated through solids, liquids and gases.

It can be propagated through solids and liquid surfaces.

 

Longitudinal waves cannot be polarised.

Transverse waves can be polarised.

 

When longitudinal waves pass through a medium, the pressure and density at any point vary between maximum and minimum values.

When transverse waves pass through a medium, there is no change in the pressure and density of the medium at any point.

 

 

Reflection of Sound Waves and Change of Phase

 

A) Reflection from a Denser Medium

  a) Transverse Wave

  • Phase changes by p radians.
  • Crest is reflected as a trough and vice versa.

  b) Longitudinal Wave

  • Phase changes by p radians.
  • Compression is reflected as a compression and a rarefaction is reflected as a rarefaction.

B) Reflection from a Rarer Medium

  a) Transverse Wave

  • No change in phase
  • A crest is reflected as a crest and a trough is reflected as a trough.

  b) Longitudinal Wave

  • No change in phase.
  • A compression is reflected as a rarefaction and vice versa.

 

 



 

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