Physics · Ch 6 — Superposition of Waves
Practical Determination of End Correction
Practical Determination of End Correction
The end correction e introduced in 6.7.1 can itself be measured experimentally, without needing to know the value of (the speed of sound) in advance, by comparing TWO pipes of the SAME diameter but different physical lengths and , and measuring their two fundamental frequencies and .
For a pipe open at both ends, Eq. (6.22)/(6.23) gives , i.e. ; substituting and and solving for e gives (Eq. 6.29).
For a pipe closed at one end, Eq. (6.15)/(6.16) similarly gives , i.e. again; substituting and gives the SAME algebraic form, (Eq. 6.30) -- the closed-pipe and open-pipe formulas for e work out identical in form, even though the underlying relation between L and l differs (l+e versus l+2e) in each case. …
Worked out. A hands-on two-part activity, not a solved numerical. Part 1: a glass tube, open at both ends, is clamped with one end dipping into a cylinder of water; sliding the tube up/down at the clamp changes the length of the AIR column trapped above the water surface (the water surface itself effectively acts like a closed end for this air column, since it is far denser than air, so this exact set-up is really a pipe 'closed' at the water end and open at the top -- this is the classic resonance-tube apparatus). Holding a vibrating tuning fork of frequency 488 Hz or 512 Hz just above the open top and adjusting the water level, the student notes the particular air-column height(s) at which the sound becomes distinctly LOUDER (resonance, when the air column's own natural frequency for that length matches the fork). Part 2: using a second, identical-frequency tuning fork sounded together with the first, the student listens for BEATS -- normally none should be heard if both forks are truly identical, but usage wears forks unevenly so beats are often heard in practice; winding a thread around one fork's tine deliberately lowers its frequency slightly, letting the student hear and study how the beat rate …