Shear Wave Velocity Calculator

Shear Wave Velocity (m/s): Shear Wave Velocity (km/s): Shear Wave Velocity (ft/s): Shear Wave Velocity (mph): Shear Wave Velocity (Hz):

1. What is a Shear Wave Velocity Calculator?

Definition: This calculator computes the shear wave velocity (\(V_s\)), the speed of transverse waves in a medium, using shear modulus and density.

Purpose: It is used in geophysics, engineering, and seismology to analyze material properties, such as soil stability or seismic wave behavior.

2. How Does the Calculator Work?

The calculator uses this formula:

\[ V_s = \sqrt{\frac{G}{\rho}} \]

Explanation: Input shear modulus and density in your chosen units. The calculator converts inputs to base units (Pa, kg/m³) and outputs velocity in m/s, km/s, ft/s, mph, and Hz.

Unit Conversions:

1 kPa = \(10^3\) Pa, 1 MPa = \(10^6\) Pa, 1 GPa = \(10^9\) Pa
1 g/cm³ = 1000 kg/m³
1 m/s = 0.001 km/s = 3.28084 ft/s = 2.23694 mph
1 m/s = \(\frac{1}{2\pi}\) Hz (for frequency context)

3. Importance of Shear Wave Velocity

Details: Shear wave velocity is vital for understanding material rigidity and seismic response. Examples include:

In geotechnical engineering, it assesses soil strength for construction.
In seismology, it helps predict earthquake ground shaking.
In material science, it characterizes elastic properties of solids.

Applications: It supports foundation design, seismic risk analysis, and material testing.

4. Using the Calculator

Tips: Enter positive values with up to 4 decimal places and select units. Results are in m/s, km/s, ft/s, mph, and Hz. Values < 0.0001 use scientific notation. Avoid zero density.

Example: For \(G = 45 \, \text{GPa} = 45 \times 10^9 \, \text{Pa}\), \(\rho = 8940 \, \text{kg/m³} (copper)\):

\(V_s = \sqrt{\frac{45 \times 10^9}{8940}} \approx 2243.6140 \, \text{m/s}\)
\(V_s \approx 2.2436 \, \text{km/s}\)
\(V_s \approx 7360.9449 \, \text{ft/s}\)
\(V_s \approx 5016.7897 \, \text{mph}\)
\(V_s \approx 357.1375 \, \text{Hz}\)

5. Related Concepts

Longitudinal Waves: Travel faster than shear waves, with speed \(V_L = \sqrt{\frac{E}{\rho}}\), where \(E\) is the elastic modulus.

Shear Modulus: Measures resistance to shear deformation, linked to elasticity via Poisson’s ratio.

Seismic Waves: Shear waves (S-waves) are slower than P-waves but critical for ground motion analysis.

6. Frequently Asked Questions (FAQ)

Q: What’s the difference between m/s, km/s, ft/s, mph, and Hz?
A: m/s, km/s, ft/s, and mph are speed units; Hz is frequency (\(f = V_s / 2\pi\)) assuming a wavelength context.

Q: Can shear modulus be negative?
A: No, it’s a positive measure of rigidity.

Q: Why does the result show zero?
A: If density is zero, division by zero occurs, so results default to zero.

Q: Why are some results in scientific notation?
A: Values < 0.0001 are displayed as, e.g., \(1.23 \times 10^{-5}\), for clarity.

Q: How do I convert units manually?
A: Use the listed conversions (e.g., 1 GPa = \(10^9\) Pa) before inputting if needed.