A PVC pipe that is one meter long is struck and the speed of sound is 345 m/s. What is the fundamental frequency (n=1) of the pipe when:

a.The pipe is open at both ends?
b.The pipe is closed at one end, open at the other?

The phenomenon is called a standing longitudinal wave, or a stationary wave.

The part of the tude Where air does not vibrate is called a node.
In the case of an open tube, the node is at mid-length of the pipe, and the open ends have maximum amplitude. So the length of the tude is half the wave-length of 2 m. The frequency is therefore 345/2=172.5 Hz.
For the tude closed at one end, the node is at the closed end, and maximum amplitude at the open end. The length of the tude is 1/4 of the wavelength of 4 m. The frequency is 345/4=86 Hz.

The following link gives a visual description of the above:
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To find the fundamental frequency of a pipe, we need to know the length of the pipe and the speed of sound in the medium (in this case, PVC).

a) When the pipe is open at both ends:
The fundamental frequency for a pipe open at both ends can be calculated using the following formula:

f = v / 2L

where:
f = fundamental frequency (Hz)
v = speed of sound (m/s)
L = length of the pipe (m)

In this case, the length of the PVC pipe is given as 1 meter, and the speed of sound in PVC is 345 m/s.

Plugging in the values, we have:

f = 345 / (2 * 1) = 172.5 Hz

Therefore, the fundamental frequency of the pipe open at both ends is 172.5 Hz.

b) When the pipe is closed at one end and open at the other:
The fundamental frequency for a pipe closed at one end and open at the other can be calculated using the following formula:

f = v / 4L

In this case, the length of the PVC pipe is still 1 meter, and the speed of sound in PVC is still 345 m/s.

Plugging in the values, we have:

f = 345 / (4 * 1) = 86.25 Hz

Therefore, the fundamental frequency of the pipe closed at one end and open at the other is 86.25 Hz.