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NEET PHYSICSWAVEMedium

Question

If we study the vibration of a pipe open at both ends, then the following statement is not true:

A

Open end will be anti-node

B

Odd harmonics of the fundamental frequency will be generated

C

All harmonics of the fundamental frequency will be generated

D

Pressure change will be maximum at both ends

Step-by-Step Solution

  1. Displacement at Open Ends: In an open organ pipe, the air particles at the open ends are free to vibrate with maximum amplitude. Therefore, displacement antinodes are formed at both open ends.
  2. Pressure at Open Ends: Since the open ends are exposed to the atmosphere, the pressure there remains constant (equal to the atmospheric pressure). This means the pressure variation (ΔP\Delta P) is zero, making the open ends pressure nodes, not pressure antinodes. Thus, the statement that pressure change is maximum at both ends is completely false.
  3. Harmonics Generated: For a pipe open at both ends, the resonant frequencies are given by fn=nv2Lf_n = n\frac{v}{2L}, where n=1,2,3,n = 1, 2, 3, \dots . This indicates that all harmonics (both odd and even) of the fundamental frequency are generated.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from WAVE. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSWAVEvibrationfollowingstatement

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