Fundamental frequency of an open pipe?

Now learn about impedance.

If you hit a ball at the tip of the bat, speed is high but force is low. The ball is not accelerated to top speed and the excess energy is reflected down the bat, perhaps breaking it. Speed divided by force gives a number called impedance, which is high for this example.

If you hit a ball near the handle of the bat, force is high but speed is low. The ball is not accelerated to top speed and the excess energy is reflected down the bat, perhaps breaking it. The impedance is low for this example.

If you hit a ball near the center of the bat, the so called sweet spot, the impedance of the ball matches the impedance of the bat and the ball gets maximum acceleration and there is no excess energy.

The open end of a pipe allows large motion but low force. (That is called a peak of the wave.) If the pipe is open at both ends, a half wave can exist along the length of the pipe, or any number of half waves as long as there is a peak at both ends.

The closed end of a pipe allows large force but no motion. (That is called a node of the wave.) If the pipe is open at the other end then a quarter wave can exist, or any odd number of quarter waves. (If the pipe is closed at both ends, you have no idea what is going on inside.)

The actual frequency at which these things take place depends on the speed of sound through the gas in the pipe, usually air, and that is not always constant. It depends mostly on temperature and humidity. At 20 °C (68 °F), the speed of sound is 343 metres per second or 1,125 ft/s.

Let's say you have a pipe 16 feet long open at both ends. The fundamental wave is 32 feet long so the frequency f = (1125 ft/s)/32 ft = 35.15625 cycles per second which we call 35.15625 Hertz. If the pipe is closed at one end, the frequency is half that much. (Because the wave is four times the length of the pipe instead of only two.)