You measure the amplitude of a longitudinal wave by finding how far the particles (or the medium’s density/pressure) move from their undisturbed, or equilibrium, condition at maximum compression or rarefaction.

What “amplitude” means here

For any wave, amplitude is the maximum displacement from equilibrium.

In a longitudinal wave:

  • Particles move back and forth along the direction the wave travels.
  • There are regions of compression (particles squashed closer) and rarefaction (particles more spread out).

Because nothing is “going up and down” like a transverse wave, we think in terms of:

  • Maximum particle displacement from their rest positions, or
  • Maximum change in density/pressure compared to normal.

Two common ways to measure amplitude

1. By particle displacement (e.g., with a slinky model)

This is the simplest to picture in a school or lab setting.

  1. Set up a slinky or spring on a table, stretched out evenly (this is the equilibrium position).
  1. Create a longitudinal pulse by quickly pushing and pulling one end along the length of the spring.
  1. “Freeze” the motion (strobe light, slow-motion video, or quick snapshot) and mark where each coil would rest.
  1. Measure, with a ruler, the largest distance that any coil has moved from its original rest position.

That maximum distance is the amplitude , typically in meters or centimeters.

In words: amplitude = biggest “back‑and‑forth shift” of any particle from where it would be if no wave passed.

2. By density/pressure variation (e.g., sound waves)

When you can’t see the particles, you often measure amplitude indirectly via pressure or density graphs.

  • For sound waves in air, you can record the pressure as a function of time with a microphone and oscilloscope.
  • On the graph, the equilibrium is the average (normal) pressure.
  • The amplitude is the maximum difference between the peak pressure (compression) and the equilibrium pressure, or between the minimum pressure (rarefaction) and equilibrium.

In this case, amplitude might be in units like pascals if you’re talking about pressure.

Quick checklist answer

When someone asks “how can you measure the amplitude of a longitudinal wave?” you can answer:

  • Look at how far particles move from their rest positions along the direction of travel, and measure the maximum displacement.
  • Or, if you have a pressure/density graph (like for sound), measure the maximum deviation from the equilibrium value on that graph.

Either way, it’s always “how far from normal” things get at the most compressed or most rarefied point.

Information gathered from public forums or data available on the internet and portrayed here.