OPOpenPithMake curiosity visiblePhysics lab / Sound

About this lab

Six experiments, one thread: how a vibration becomes the sound we hear.

Sound is made by vibrating objects and needs a material to carry it to the ear. The first two experiments look at travel: without air the sound cannot get out, and in different materials it travels at different speeds. The middle three look at the three features of a sound: pitch is set by frequency, loudness by amplitude and distance, timbre by the wave shape. The last one puts sound to use: listen for the echo and measure a distance.

Every reading and every wave comes from one physics model, not from a pre-drawn animation. The picture is in slow motion; with Sound on you hear the model’s frequency in real time, and your device volume is not the physical sound level.

What each experiment shows

Six common ideas that the data overturns

  • “In a vacuum the bell stops vibrating” — the hammer keeps striking with the same swing; the less air in the jar, the less sound gets out. At the pump’s limit only about 28 dB is left, carried out through the base.
  • “Sound is fastest in air” — over the same 1.2 m: steel 0.20 ms, water 0.81 ms, air 3.50 ms. Solids carry sound fastest.
  • “If you see it vibrate you can hear it” — with more than about 20 cm over the edge, the ruler vibrates below 20 Hz: visible but silent. Plucking harder only raises the amplitude; the frequency stays the same.
  • “Twice as far, half as loud” — doubling the distance lowers the level by only 6 dB; sound level is logarithmic, not a linear volume.
  • “Same pitch and loudness means the same sound” — four sources at 440 Hz, equally loud, still have different wave shapes because their harmonics are mixed differently.
  • “Just remember 340 m/s for echo ranging” — at 0 °C, using 340 m/s overestimates the distance by about 2.7 %. Soft absorbing materials make the echo much weaker.

Model and sources

Model and sources

  • Bell jar: the sound pressure inside is proportional to the air density and stays proportional after passing the glass, so L = L0 + 20 lg(P/P0); the sound through the base is added by energy.
  • Speed of sound: steel 5960 m/s, water 1480 m/s; air v = 331 m/s × √(T/273 K).
  • Ruler: first bending mode of a cantilever, f = (1.875² / 2π)·√(E·t² / 12ρ) / L², with steel E = 210 GPa, ρ = 7.8×10³ kg/m³, 1 mm thick.
  • Loudness: a point source in free space, L = Lref + 20 lg(A/Aref) − 20 lg(r / 1 m); paper bits jump h = (2πfA)² / 2g.
  • Timbre: harmonics of one fundamental added together and scaled to the same RMS value; the check script recovers the harmonic amplitudes with a Fourier transform.
  • Echo: round trip t = 2d / v, distance s = vt / 2.

These are teaching assumptions, used only to compare sizes, not measured values: the bell’s 78 dB at 1 m, 28 dB through the base, the pump’s time constant and ultimate pressure, the drum’s 88 dB at 1 m, the drum’s 110 Hz fundamental, the harmonic mix of the four instruments, the ruler’s damping and the reflection coefficients of the three boards. Distances in the loudness and echo experiments are compressed in the picture; the readings give the true values.

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