Cornell Note | Resonance Tube & Sound Speed Measurement — Notes

type: cornell_note | topic: resonance-tube, waves

Apparatus Reference (Wikimedia Commons): https://commons.wikimedia.org/wiki/Special:FilePath/Resonance_tube.jpg?width=600

Cue Column | Note-Taking Column

Cue	Notes
What is measured?	Speed of sound in air
First resonance	l_{1} + e = λ/4 → air column = quarter wavelength
Second resonance	l_{2} + e = 3λ/4 → air column = three-quarter wavelength
Key formula	v = 2f(l_{2} − l_{1}) — eliminates end correction
Why preferred?	Subtracting l_{1} from l_{2} cancels the same end correction e from both
End correction formula	e = (l_{2} − 3l_{1})/2
If only l_{1} used	v = 4f(l_{1} + e) ≠ 4fl_{1} — end correction is NOT eliminated
Dimensional check	v: [ $LT^{-1}$ ], f: [ $T^{-1}$ ], l: [L] → [ $T^{-1}$ ][L] = [ $LT^{-1}$ ] ✓
Mnemonic	"Twelve Eliminates End" — Two lengths eliminate end correction
SI units	v: m/s, l_{1}, l_{2}: m, f: Hz

Summary

Resonance tube measures speed of sound by using both resonance positions to cancel end correction. v = 2f(l_{2}−l_{1}) is the preferred formula. e = (l_{2}−3l_{1})/2 gives the end correction.