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?

To determine the fundamental frequency of a PVC pipe, we need to consider the different boundary conditions - whether the pipe is open or closed at one or both ends. The fundamental frequency (n=1) corresponds to the first harmonic, which is the lowest resonant frequency produced by the pipe.

a. When the pipe is open at both ends, it creates an open-open boundary condition. For this case, the fundamental frequency can be calculated using the formula:

𝑓 = 𝑣/2𝐿

where 𝑓 is the frequency, 𝑣 is the speed of sound, and 𝐿 is the length of the pipe.

Substituting the given values, we have:

𝑓 = 345 m/s / (2 * 1 m)
𝑓 = 172.5 Hz

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

b. When the pipe is closed at one end and open at the other, it creates a closed-open boundary condition. In this case, the fundamental frequency can be calculated using the formula:

𝑓 = 𝑣/4𝐿

Again, substituting the given values:

𝑓 = 345 m/s / (4 * 1 m)
𝑓 = 86.25 Hz

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