# Speed of Sound in Solids Calculator

By Rahul Dhari
Last updated: Nov 24, 2021

The speed of sound in solids calculator can be used to estimate the speed of sound waves propagating through different solid mediums. Imagine you strike a hammer at an end of a long rod, the generated sound wave will travel through the long rod till the other end and then travel back to you. This calculator will help you with the wave propagation speed or in other words the speed of sound in materials such as solids like a copper or steel rods.

The speed of sound in solids is estimated based on the density and modulus of elasticity of the material. In case you only know the shear modulus of the material you can head over to the Poisson's ratio calculator to find the respective modulus of elasticity. Scroll down to understand the formula behind the calculations.

## What is a sound wave and how to calculate the speed of a sound wave?

The mechanical wave generated from the vibration of particles in a medium is known as a sound wave. The speed of a sound wave is the distance travelled by the energy of the wave per unit of time. The speed of a sound wave depends on the properties of the medium in which it is traveling. If the sound wave is traveling through a long cylindrical rod of material A having a density, ρ and modulus of elasticity, E, the speed of the sound wave can be written as:

c = √(E / ρ)

## Factors affecting speed of sound

The sound wave propagation speed is affected by different properties of the medium. For example, the stiffness and rigidity of material would have an impact over the speed of sound wave. The higher the modulus of elasticity, the higher the speed of sound. On the other hand, denser materials will result in slower wave speeds. However, the modulus of elasticity has higher influence over the speed of sound compared to density. Therefore, when comparing the speed of sound across different states it can be observed that:

Vsolids > Vliquid > Vgas.

The speed of sound is also affected by temperature of the medium - check out our speed of sound calculator for more detailed information on this topic!

## Using the speed of sound in solids calculator.

Follow the steps mentioned below to estimate the speed of sound wave in a solid:

• Step 1: Set the units as per the data available. You can also convert the speed in appropriate units using our speed conversion tool.

• Step 2: Enter the density of material. If you wish to convert the density into other units click here.

• Step 3: Input the modulus of elasticity.

• Step 4: The speed of sound in solids calculator will provide the speed of sound in the material.

Alternatively, if you know the material and its on our list, simply select it from the material drop-down menu to display all its properties.

## Example: Estimate the speed of sound in material.

Let's use the speed of sound in solids calculator in an example problem. Find the speed of sound in a solid long copper rod, given the density of copper is 8,940 kg/m3 and modulus of elasticity is 117 GPa.

• Step 1: Set the calculator units for density and modulus of elasticity as kg/m3 and GPa respectively.

• Step 2: Enter the density of copper as 8,940 kg/m3.

• Step 3: Input the modulus of elasticity as 117 Gpa.

• Step 4: The sound wave speed calculator will return the wave speed in m/s as 3,618 m/s.

Rahul Dhari
Density of material
kg/m³
Modulus of elasticity
Pa
Speed
m/s
Speed of sound in certain solids
Material
Custom ▾
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