A 110 cm long pipe is closed at one end. What is the fundamental frequency of the pipe? The speed of sound in air is 340 m/s.

Answer 1

At the closed end of the pipe the air molecules cannot vibrate, as sound is longitudinal.

Therefore there is a node at that end.

In contrast, the molecules at the open end can vibrate.

Therefore the longest wavelength occurs when just 1/4 of the wave is inside the pipe.

Therefore the fundamental wavelength is λ = 440cm = 4.4 m.

Given that the speed of sound v = 340 m/s,

the fundamental frequency

f = v/λ = 340/4.4 = 77.3 Hz