# Shear Wave Velocity Calculator

By Rahul Dhari
Last updated: May 04, 2021

The shear wave velocity calculator determines the velocity of a shear wave as it moves through a body. This velocity is calculated based on the two main parameters or properties of a material, which are density and shear modulus. An example of shear waves is a seismic wave. That's why shear wave velocity is a key parameter in soil analysis in the area of geotechnical evaluation of ground sites. The faster the velocity, the lesser the ground is shaking. Read on to understand what is shear wave velocity and how to calculate shear wave velocity.

## What is a shear wave?

A shear wave is a type of wave occurring in bulk mediums when the particles oscillate perpendicular to the direction of wave propagation. The shear wave is caused by a shear type of loading. The shear forces cause a change in the shape of the bulk medium and do not cause any change in the volume of the body. These forces occur in pairs with either acting along the face of the medium. The shear wave is also known as an S-wave. We define the shear wave velocity as the square root of the ratio of shear modulus (modulus of rigidity) to the density of material. The velocity of the shear wave `Vs` in the medium having shear modulus `G` and density `ρ` can be written using the shear wave velocity formula:

`Vs = √(G / ρ)`

The shear wave velocity is about half of the longitudinal wave. The speed of longitudinal waves `VL` depends on modulus of elasticity `E` and density.

`VL = √(E / ρ)`

## How to use the shear wave velocity calculator?

Follow the steps below to find shear wave velocity:

• Step 1: Enter the shear modulus of the bulk medium.
• Step 2: Input the density of the material.
• Step 3: The shear wave velocity calculator will return the answer.

## Example: What is shear wave velocity in a medium?

Now, let's try an example. Find the shear wave velocity for wave propagation in a copper rod.

You can tap on the `advanced mode` of the calculator to directly choose the material from the list. Alternatively, you can input the values of shear modulus and density of copper which are `45 GPa` and `8940 kg/m3`, respectively.

• Step 1: Enter the shear modulus, `G = 45 GPa`.

• Step 2: Input the density of material, `ρ = 8940 kg/m3`.

• Step 3: The calculator will now use the shear wave velocity formula:

`V = √(G / ρ) = √(45,000,000,000 / 8940) = 2243.6 m/s`

The velocity of shear wave in copper is `2.244 km/s`.

## FAQ

### What is shear wave?

The waves generated by a pair of shear forces acting along the opposite faces of a body is known as a shear wave. The particles in this wave oscillate perpendicular to the direction of wave propagation.

### What is shear wave velocity?

The velocity at which shear waves propagate through bulk matter is called the shear wave velocity. It depends on the shear modulus and density of the material. Mathematically, that's: `Vs = √(G / ρ)`.

### How do I find shear wave velocity?

To find shear wave velocity:

1. Divide the shear modulus by the density of the material.
2. Find the square root of this ratio. Mathematically, that's: `Vs = √(G / ρ)`

### What is velocity of shear wave in a titanium body?

The velocity of the shear wave in titanium is `3018.5 m/s`, which you can find by dividing the shear modulus, `G = 41 GPa` by density, `ρ = 4500 kg/m3` and then taking the square root.

Rahul Dhari
Shear modulus
psi
Density
lb/cu ft
Shear wave velocity
ft/s
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