OPOpenPithMake curiosity visiblePhysics lab / Waves

About this lab

Five experiments, one thread: a vibration happens in one place, and a wave carries it far away.

The first three look at a single oscillator: what sets its period, and which driving frequency it responds to most. The last two look at a chain of them: how motion passes from one to the next to make a wave, and how two opposite waves add to make a standing wave.

Every reading, curve and table row comes from the same physical model, not a pre-drawn animation. Change one parameter and all the data is recalculated together.

Five findings

Run the experiments and you will arrive at these five statements.

  1. A spring oscillator’s period does not depend on amplitude: with k = 20 N/m and m = 100 g, T ≈ 0.444 s whether the amplitude is 1 cm or 5 cm.
  2. A pendulum’s period does not depend on the bob’s mass. At 80 cm and 5°, T ≈ 1.796 s, giving g ≈ 9.79 m/s²; at 60° the period is about 7.3 % longer and the small-angle formula no longer holds.
  3. Faster driving is not always stronger: with medium damping the steady amplitude is about 4.19 cm at 1 Hz, about 0.62 cm at 0.6 Hz and only about 0.32 cm at 1.5 Hz.
  4. When a wave passes, each particle only vibrates in place. At 0.6 m/s and 1 Hz the wavelength is 60 cm; double the frequency and the wavelength halves while the speed stays.
  5. With 200 g hanging, the string forms steady standing waves only at whole multiples of about 15.7 Hz; at 31.3 Hz there are 2 antinodes and the nodes are 50 cm apart.

Model and sources

Model and sources

  • Spring oscillator: an ideal light spring with no damping; the light gate sits at the rest position and times to 0.1 ms.
  • Pendulum: the exact period comes from the arithmetic–geometric mean, the swing from RK4 integration; air drag and the thread’s mass are ignored.
  • Driven oscillator: natural frequency 1 Hz, eccentric drive amplitude 4 mm, damping 0.15, 0.3 and 0.6 s⁻¹; integrated with RK4 for 40 s from rest.
  • Mechanical wave: the source starts simple harmonic motion at t = 0 with 4 cm amplitude; energy loss and reflection at the far end are ignored.
  • Standing wave: 1 m of string, 2 g/m, 2 mm drive; the steady state uses a complex wavenumber with light damping.

g is the textbook 9.8 m/s²; the Moon’s 1.62 m/s² and Mars’s 3.73 m/s² come from the NASA planetary fact sheets. The damping coefficients, drive amplitudes and string damping are teaching assumptions for comparison only, not measurements. Arrow lengths are schematic only.

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