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An open pipe is one where both ends are open to the air, allowing sound waves to pass through easily. In such pipes, the ends act as points of maximum air displacement, or antinodes. This is because the air can freely move at these points. For standing wave patterns, this characteristic affects how harmonics, or the natural frequencies of the pipe, are structured.

The fundamental frequency, or first harmonic, creates a wave pattern with just one node, which is a point of zero displacement, located exactly in the middle of the pipe. The distance between each node and antinode in this case is half of the pipe length. For a pipe length of 1.20 m, the node is at the midpoint, specifically at 0.60 m.

If we move to the first overtone, which is the second harmonic, this pattern changes. In this case, there are two additional nodes, dividing the pipe into thirds. This results in displacement nodes located at 0.40 m and 0.80 m along the pipe. As you progress to higher harmonics, more nodes form along the pipe, continuing this pattern.

In contrast to open pipes, closed pipes have one end sealed and the other open. The closed end of the pipe is a displacement node because the air cannot move freely, while the open end remains a displacement antinode, where maximum movement occurs.

The standing wave pattern for the fundamental frequency in a closed pipe is a quarter wavelength, meaning the pattern from the closed end to the first antinode occupies only a quarter of the wave cycle. For a pipe 1.20 m long, there is a node at the closed end (0 m), and the length accommodates a quarter wave for the first harmonic.

The first overtone in a closed pipe involves adding three quarters of the wavelength to the existing pattern, forming a new displacement node at approximately 0.40 m from the closed end. This pattern means that closed pipes do not have straightforward integer multiples for harmonics, unlike open pipes, and leads to differences in the possible frequencies produced. This unique configuration is why closed pipes are often used in musical instruments like clarinets or certain organ pipes.

Displacement nodes are essential in understanding standing waves, as they are points along the medium where there is no movement at all. These nodes occur due to the destructive interference of waves traveling in opposite directions, causing them to cancel out at specific points.

In open pipes, displacement nodes appear in regular patterns along the pipe. For the fundamental frequency in an open pipe, there's a single displacement node in the center. For the first overtone, nodes appear at one-third and two-thirds along the pipe.

In closed pipes, the first displacement node is always at the closed end because air cannot move here. For the first overtone, an additional node will appear further along the pipe, marked by a decrease in displacement as the wave reflects back towards the open end.

Pressure nodes are different from displacement nodes; these are the points of constant air pressure, where changes in pressure constructively or destructively interfere to create no variation.

In open pipes, pressure nodes occur at the very ends, where there is the greatest air movement, corresponding to displacement antinodes. Between the nodes of displacement, pressure nodes can be located along the pipe equally spaced.

For closed pipes, the closed end is a pressure antinode due to no air fluctuations and a maximum pressure level, while the open end is a node of pressure where pressure varies minimally. In terms of harmonics, a pressure node is halfway between two displacement nodes in an open pipe, whereas, in a closed pipe, it coincides with the first displacement node. These relationships help define how sound waves behave in pipes and dictate the musical notes possible from various pipe instruments.