An open pipe of length l vibrates in a fundamental mode. The pressure variation is the maximum at:
(A) 1/4 from ends
(B) middle of the pipe
(C) ends of the pipe
(D) at 1/8 from the end of the pipe

In an open pipe vibrating in its fundamental mode, the sound waves inside the pipe produce standing waves. The pressure variation in a standing wave depends on the points of maximum and minimum displacement (antinodes and nodes) and maximum pressure (antinodes) and minimum pressure (nodes).
Key characteristics of the fundamental mode:
• In the fundamental mode of vibration, the pipe behaves such that there are:
o Pressure nodes at the ends of the pipe (since the pipe is open at both ends, the air molecules at the ends have maximum displacement, creating nodes of pressure).
o Pressure antinodes at the open ends of the pipe where the displacement of air is maximum and the pressure variation is at its highest.
Now, in terms of pressure:
• The pressure maximum (antinodes) is at points where the displacement is minimum.
• The pressure minimum (nodes) occurs at the points of maximum displacement of air particles.
For an open pipe vibrating in its fundamental mode:
• The pressure variation is maximum at the middle of the pipe and minimum at the ends.
Hence, the correct answer is: (B) middle of the pipe.
Explanation:
• In the case of a pipe open at both ends, the standing wave pattern formed has:
o Antinode (maximum pressure variation) at the center of the pipe.
o Node (no pressure variation) at both ends of the pipe.
Thus, the pressure variation is maximum at the middle of the pipe in the fundamental mode of vibration.