# Speed of Sound using Resonance

The aim of my experiment was to determine the speed of sound using the theory behind resonance; that, when a vertical pipe open at both ends is partially submerged in water, and a tuning fork vibrating at an unknown frequency is placed near the top of the pipe, and when the length L of the air column is adjusted by moving the pipe vertically, the sound waves generated by the fork are reinforced when L corresponds to one of the resonance frequencies of the pipe.

I later realised that the bottom end of the air column is closed by the water level. Since water is more dense than air, the water surface represents (and only represents) a rigid wall. It is thus assumed that the air molecules are so great confined at this end that they cannot vibrate. This is not the case however. Not all waves reflect off the water barrier.

Would this affect my results? If so, how?

## 2 Answers

The water is a reasonably good reflector of sound and so the way the interpretation of your observations might be affected is shown below.

The bottom of you tube will be a displacement node (no vibrations) and the top of the tube (or more accurately just above the top) is a displacement antinode so the length of the tube at the lowest resonance position is $\frac {\lambda}{4}$ whereas for a tube open at both ends the lowest resonance occurs when the tube length is $\frac {\lambda}{2}$.

I wrote "more accurately just above the top " because there is what ia called an "end correction" to be made in that to the sound the tube seems to be longer by that amount that the tubes actually physical length.

• Why is the node at the top of the tube actually just above the top? – GoodChessPlayer Feb 9 '16 at 15:08
• @GoodChessPlayer It is a displacement antinode at the open end. I simple terms when you get right to end of the tube the air movement is still not total free os the presence of the tune. More here en.wikipedia.org/wiki/End_correction also giving the end correction as 0.3 $\times$ diameter of the tube. – Farcher Feb 9 '16 at 15:54

I hope I'm wrong, but I think your experiment will be difficult to execute. Consider the info in this question, for example. You can excite a number of resonant frequencies, including in some cases a sub-resonance, so I'm not sure how you can identify the wave speed solely on the existence of a resonance. Maybe if you run thru several resonances you can find a "least common denominator" to infer the fundamental wavelength.