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MHT-CET : Physics Entrance Exam

MHT - CET : Physics - Stationary Waves Know More

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  • A stationary wave does not transport energy.
  • Stationary waves can be formed by both transverse as well as longitudinal waves.
  • When a stationary wave is formed in a medium, different particles of the medium oscillate with different amplitudes, different speeds and same phase. Some particles do not oscillate at all.
  • Alternate nodes and antinodes are formed.
  • Frequency of the pth harmonic is equal to the frequency of (p - 1)th overtone of a string.
  • According to the law of length, n1l1 = n2l2
  •  

According to the law of tension,

n1

=

n2

 

  •  

According to the law of mass,

n1

=

n2

 

  • Melde's experiment demonstrates the formation of stationary waves.
  • For both longitudinal and transverse positions, p2T = constant.
  • For a pipe closed at one end,

n =

V

 (Without end correction)

4l

=

V

 (With end correction)

2(l + 0.3d)

  •  
  • For a pipe open at both ends,

n =

V

 (Without end correction)

2l

=

V

 (With end correction)

2(l + 0.6d)

  •  
  • To eliminate end correction, in resonance tube,

length at first resonance l1 + e =

l

4

Length at second resonance l2 + e =

3l

4

\ l2 - l1 =

l

2

  • l = 2 (l2 - l1)
    \ V = 2n(l2 - l1)
  • Regnault suggested that the end correction should be applied since antinode is not formed at the open end but slightly above it.
  • Intensity is directly proportional to square of amplitude.
  • When the frequency of the applied force is the same as the fundamental frequency of the driven system, the resonance is known as principal resonance.
  • When the frequency of the applied force is equal to any overtone of the driven system, the resonance is known as secondary resonance.
  • For longitudinal stationary waves, displacement nodes are called pressure antinodes while displacement antinodes are called pressure nodes. At pressure nodes, pressure changes are minimum, while at pressure antinodes, pressure changes are maximum.

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