MHT-CET Physics Crash Course “End Correction and Its Determination” Class 12

“End Correction and Its Determination” MHT-CET Class 12 Physics Crash Course | Chapter – Superposition of Waves

In this session G.S. Khairnar discussed the theory and MCQ’s of “End Correction and Its Determination”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.

End Correction and Its Determination:-

Hello dear students in previous article we have learnt about the modes of vibration of air column in pipe a) closed at one end and b) open at both ends. We have derived the formulae for the fundamental frequencies and harmonics in both the cases which can be written as,

1) Pipe closed at one end-

Only odd harmonics are present in vibrations of air column when pipe is closed at one end.

2) Pipe opens at both ends-

All harmonics(odd and even) are present in vibrations of air column when pipe is open at both end.

Now let’s learn the concept of end correction….!

When air column forms in pipe closed at one end or open at both ends, to satisfy the boundary conditions antinodes are always formed at open end as there is more scope for vibration of particles. But in practice, antinodes forms beyond the open end due to which error in the calculations of pipe can be arose. To minimize these errors, Sir Laplace’s proposed the concept of adding the term called end correction.

The distance between open end of pipe and exact position of antinode is called as end correction (e),

According to Reynolds’s,

e =0.3d

Where d is internal diameter of pipe.

Hence,

Corrected length of air column = Length of air column in pipe + end correction.

∴ L = l+0.3d

Expressions for the end correction….!

  • For pipe closed at one end:

The fundamental frequency can be given as

  • For pipe open at both ends:

  • Limitations of end correction:-

  1. Inner diameter of tube must be uniform throughout its length.
  2. Effect of flow of air outside tube is to be neglected.
  3. Effect of temperature is to be neglected.


End Correction and Its Determination:-

Let’s solve some MCQ’s….!

Q.1) In the expression for the corrected length of air column , the term ‘d’ represents..

a) distance between nodes

b) distance between antinodes

c) distance between nodes and antinodes

d) internal diameter of pipe

Answer

d) internal diameter of pipe

Q.2) End correction should be e =0.3d, this was proposed by

a) Laplace

b) Reynolds

c) Poisson

d) Bernoulli

Answer

b) Reynolds

Q.3) End correction for the pipe closed at one end is given as….

Q.4) End correction for the pipe open at both end is given as….

Q.5) Vibrating lengths of pipe closed at one end are 24.5 cm and 30.5 cm having corresponding frequencies of 324 Hz and 288 Hz respectively, end correction is

a) e=0.235 mm

b) e=0.235 cm

C) e=0.235 m

d) e=0.235 μm

Answer

c) e=0.235 m


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