Question: Standing sound waves are produced in a pipe that is 1.20 m long. For the fundamental and first two overtones, determine the locations along the pipe (measured from the left end) of the displacement nodes and the pressure nodes if

(a) the pipe is open at both ends and

(b) the pipe is closed at the left end and open at the right end.

The pipe is 1.20 m long. And standing waves are being produced in it. This is open at both ends.

The formation of the standing waves in the pipe takes place in a way that when the pipe is open at both ends will have an antinode at both ends and a node in the middle of the pipe for principal frequency, and then we can calculate for the number and location of the first and second overtones.

The waves in the pipe can be drawn,

The location of displacement nodes (N) is:

In fundamental:

There will one only one node, and it will be at the center that is at 0.60 m from the left.

In the first overtone:

There will be two nodes, which means the positions will be 0.30 m and 0.90 m from the left.

In the second overtone:

There will be three nodes, which means the positions will be 0.20 m, 0.60 m, and 1m from the left.

The location of pressure nodes/anti-nodes (A) is,

In fundamental:

There will be two anti-nodes, and they will be at 0 m and 1.20 m from the left.

In the first overtone:

There will be three anti-nodes, which means the positions will be 0 m, 0.60 m, and 1.20 m from the left.

In the second overtone:

There will be four anti-nodes, which means the positions will be 0 m, 0.40 m, 0.80 m, and 1.20 m from the left.

Thus, the location of displacement nodes for fundamental is 0.60 m from the left; for the first overtone, it is 0.30 m and 0.90 m from the left, and for the second overtone, it is 0.20 m, 0.60 m, and 1m from the left. The location of pressure nodes for fundamental is 0 m and 1.20 m from the left; for the first overtone, it is 0 m, 0.60 m, and 1.20 m from the left, and for the second overtone, it is 0 m, 0.40 m, 0.80 m, and 1.20 m from the left.