Geology & Earth ScienceGeophysicsA-Level
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P-Wave Velocity (Primary Waves) Calculator

The velocity of compressional waves traveling through an elastic medium.

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P-Wave Velocity

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Overview

Primary waves (P-waves) are compressional seismic waves that travel through the Earth's interior by pushing and pulling material in the direction of propagation. This equation mathematically links their velocity to the elastic properties—bulk and shear moduli—and the mass density of the medium through which they move.

Symbols

Variables

v = P-Wave Velocity, K = Bulk Modulus, G = Shear Modulus, = Density

P-Wave Velocity
m/s
Bulk Modulus
Pa
Shear Modulus
Pa
Density

Apply it well

When To Use

When to use: This equation is used to calculate the speed of the fastest seismic waves through Earth's layers, assuming the material behaves as an isotropic elastic solid. It is fundamental in earthquake seismology and reflection seismology for interpreting subsurface structures based on seismic travel times.

Why it matters: Since P-waves are the first to arrive at seismic monitoring stations, their velocity is critical for early warning systems that alert cities before more damaging waves arrive. Measuring these velocities allows geophysicists to determine the physical state of the Earth's interior, such as identifying the liquid nature of the outer core where the shear modulus drops to zero.

Avoid these traps

Common Mistakes

  • Using only one modulus in the formula.
  • Incorrect units for density (kg/ is standard).

One free problem

Practice Problem

A granite sample has a bulk modulus (K) of 35 GPa and a shear modulus (G) of 25 GPa. Given a density (rho) of 2700 kg/m³, calculate the velocity (v) of the primary wave passing through this rock.

Bulk Modulus35000000000 Pa
Shear Modulus25000000000 Pa
Density2700 kg/m^3

Solve for:

Hint: Calculate the sum of K and 4/3 times G first, then divide by density before taking the square root.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Lowrie, Fundamentals of Geophysics
  2. Stein and Wysession, An Introduction to Seismology, Earthquakes, and Earth Structure
  3. Wikipedia: P-wave
  4. Halliday, Resnick, Walker, Fundamentals of Physics
  5. Britannica: Seismic wave
  6. Shearer, P. M. (2009). Introduction to Seismology (2nd ed.). Cambridge University Press.
  7. P-wave. (n.d.). In Wikipedia. Retrieved from https://en.wikipedia.org/wiki/P-wave
  8. Structure of the Earth. (n.d.). In Wikipedia. Retrieved from https://en.wikipedia.org/wiki/Structure_of_the_Earth