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AP Physics · enrichment

Waves, Sound & Resonance — Visual Lab

Module 4. A column of air has a built-in set of favorite frequencies. Drive a tube with a loudspeaker, sweep the frequency, and watch the air snap into a standing wave the instant you hit a harmonic — nodes locked in place, antinodes swinging hardest, the tube ringing.

Interactive Lab Module 04 · Resonance Tube Standing Waves & Harmonics

A standing wave is what you get when a wave reflects off the far end of a tube and overlaps itself. At most frequencies the reflection and the drive fight each other and nothing builds. But at special harmonic frequencies the two line up perfectly: fixed nodes where the air never moves, and antinodes where it swings the most. Those frequencies are set by the tube's length and whether its far end is open or closed. Drive the lab below and find them.

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Resonance Tube Lab

Set the tube length \(L\) and the drive frequency \(f\), and choose an open–open or open–closed air column. When \(f\) matches a harmonic the tube resonates — the standing wave locks in and the status banner lights up. Hit Snap to nearest harmonic or click a frequency in the ladder to land exactly on a resonance.

Orientation

What you're seeing

  • The loudspeaker drives the open left end. It pushes the air back and forth at the frequency \(f\) you set with the slider.
  • The curve is air displacement. It shows how far the air at each point is pushed from rest. Dots mark nodes (no motion); dashed bars mark antinodes (maximum motion).
  • Open ends are antinodes; a closed end is a node. Air is free to slosh at an open end but pinned against a closed wall — that's what changes which harmonics fit.
  • The banner tells you the truth. Off resonance the motion is faint and washed out; on resonance it locks into a clean pattern and the banner turns on.
  • The ladder lists this tube's harmonics. Open–open tubes get every harmonic \(1,2,3,\dots\); open–closed tubes get only the odd ones \(1,3,5,\dots\).
Investigation

Try this

  1. Start open–open at \(L=1.00\) m. Sweep \(f\) slowly upward. The tube stays quiet, then suddenly rings at \(\approx 172\) Hz, again near \(343\) Hz, again near \(515\) Hz — the harmonic series.
  2. Switch to open–closed. Notice the fundamental drops to \(\approx 86\) Hz (half of before) and the even harmonics vanish — only \(1,3,5,\dots\) survive.
  3. Hold \(f\) fixed and stretch \(L\). A longer tube has lower harmonics, so the same frequency now resonates at a higher mode number \(n\) — more nodes fit inside.
  4. Hit "Snap to nearest harmonic." Watch \(f\) jump exactly onto \(f_n=\tfrac{nv}{2L}\) (or \(\tfrac{nv}{4L}\)) and the standing wave click into place.
✓

Worked Examples

Two of the moves this module asks for most: finding a tube's harmonic frequencies, and converting between frequency, period, and wavelength.

Example 1 — Harmonics of an open–open vs. open–closed pipe

Harmonic series for an air column · \(v = 343\) m/s

A pipe is \(L = 0.50\) m long. Find its fundamental and the next two harmonics — first as an open–open pipe, then as an open–closed pipe.

  1. Open–open fundamental. \(f_1 = \dfrac{v}{2L} = \dfrac{343}{2(0.50)} = 343\) Hz.
  2. All integer harmonics follow. \(f_n = n f_1\), so \(f_2 = 686\) Hz and \(f_3 = 1029\) Hz.
  3. Open–closed fundamental. Now \(f_1 = \dfrac{v}{4L} = \dfrac{343}{4(0.50)} = 171.5\) Hz — half the open–open value.
  4. Only odd harmonics survive. \(f_n = n f_1\) with \(n = 1,3,5\): \(f_3 = 514.5\) Hz and \(f_5 = 857.5\) Hz.
Answer: open–open gives \(343,\ 686,\ 1029\) Hz; open–closed gives \(171.5,\ 514.5,\ 857.5\) Hz. Check both in the lab by setting \(L=0.50\) m and snapping.

Example 2 — From frequency to period to wavelength

\(T = 1/f\) and \(\lambda = v/f\) · \(v = 343\) m/s

A tuning fork sounds at \(f = 256\) Hz (middle–ish C). Find its period and the wavelength of the sound it makes in air.

  1. Period is the reciprocal of frequency. \(T = \dfrac{1}{f} = \dfrac{1}{256} \approx 0.00391\) s \(= 3.91\) ms.
  2. Wavelength uses the wave-speed relation. \(v = f\lambda\), so \(\lambda = \dfrac{v}{f}\).
  3. Substitute. \(\lambda = \dfrac{343}{256} \approx 1.34\) m.
  4. Sanity check. Audible sound (\(20\)–\(20{,}000\) Hz) has wavelengths from \(\sim 17\) m down to \(\sim 1.7\) cm — \(1.34\) m fits right in the middle.
Answer: \(T \approx 3.91\) ms and \(\lambda \approx 1.34\) m. The lab's readout shows the same \(T\) and \(\lambda\) for any frequency you set.
Why it matters Every instrument that makes a pitch — a flute, an organ pipe, a trombone, a bottle you blow across, even your own vocal tract — is an air column resonating at its harmonics. The same resonance idea explains why a wine glass shatters at exactly one note, why a bridge can sway itself apart in the wind, and how an MRI or a radio tunes to one frequency out of millions. Master the resonance tube here and the standing waves on strings, the Doppler shift, and the physics of music and noise all open up.
About this course This lab targets the Waves & Sound ideas of AP Physics 1 — the wave-speed relation \(v = f\lambda\), standing waves, the harmonic series, and resonance in open and closed air columns. AP Physics · enrichment — not a TEKS-graded course. It is offered as supplemental, college-level practice and is not part of the Texas Essential Knowledge and Skills sequence; nothing here is scored toward a TEKS grade. Use it to stretch, preview a first-year college physics class, or prepare for the AP exam — not as a graded requirement.
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Key Vocabulary

The precise words a physicist uses to describe what the lab is doing.

Standing wave

A wave pattern that appears to stay still: a forward wave and its reflection overlap so that some points never move and others swing in place.

Node & antinode

A node is a point of zero motion; an antinode is a point of maximum motion. They alternate, spaced half a wavelength apart.

Harmonic \(f_n\)

One of a tube's resonant frequencies. Open–open: \(f_n = \dfrac{n v}{2L}\) for \(n=1,2,3,\dots\); open–closed: \(f_n = \dfrac{n v}{4L}\) for odd \(n\) only.

Fundamental \(f_1\)

The lowest harmonic — the natural pitch you hear most strongly. Every other harmonic is an integer (or odd-integer) multiple of it.

Resonance

The dramatic build-up of amplitude when a driving frequency matches a natural frequency of the system. It's why the tube suddenly "sings."

Wave-speed relation

\(v = f\lambda\): a wave's speed equals its frequency times its wavelength. In air, \(v \approx 343\) m/s, so frequency and wavelength trade off.

Standards in this lab

AP Physics 1 — Waves & Sound

This lab works the Waves & Sound strand of AP Physics 1: the wave-speed relation \(v=f\lambda\), superposition and standing waves, the harmonic series of open and closed air columns, and resonance. The Doppler shift and beats live in this same module's practice set.

AP 1 · Wave Speed v = fλ Standing Waves Harmonic Series Open & Closed Pipes Resonance

Enrichment, not TEKS. Topic structure follows the College Board AP Physics 1 framework (Waves & Sound). This is supplemental college-level practice and is not a TEKS-graded course; nothing here is scored toward a Texas Essential Knowledge and Skills grade.

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AP Physics · enrichment — a supplemental, college-level course offered alongside the Mathematical Architects sequence. Topic structure follows the College Board AP Physics 1 framework. Not a TEKS-graded course. "AP" and "Advanced Placement" are registered trademarks of the College Board, which is not affiliated with and does not endorse this site.