Speed of Sound in Solids Calculator
Calculate speed of sound in solids from Young's modulus and density. Get P-wave and S-wave speeds for steel, aluminum, copper, and more with interactive charts.
Formula: vlong = √(E/ρ) | vshear = √(G/ρ) | G = E / 2(1+ν)
About This Calculator
The Speed of Sound in Solids Calculator computes the velocity at which sound waves propagate through solid materials. Unlike gases and liquids, solids support two types of elastic waves: longitudinal (compression) waves and shear (transverse) waves. These are analogous to P-waves and S-waves in seismology.
The longitudinal wave speed is calculated using the formula v = √(E/ρ), where E is Young's modulus (stiffness) in pascals and ρ is density in kg/m³. The shear wave speed uses v = √(G/ρ), where the shear modulus G is derived from Young's modulus using Poisson's ratio. Sound travels fastest in stiff, lightweight materials — diamond tops the list at approximately 12,000 m/s, while rubber transmits sound at only 30-60 m/s.
How it works
Select a predefined material from the dropdown — steel, aluminum, copper, brass, titanium, concrete, wood, glass, nylon, rubber, gold, silver, and more. Each material has its Young's modulus and density preloaded from standard engineering tables. For custom materials, enter your own values. The calculator displays both longitudinal and shear wave speeds, a comparison bar chart, and a detailed breakdown of material properties.
Applications
This calculator is useful for engineers selecting materials for acoustic applications, seismologists studying wave propagation through Earth's crust, NDT (non-destructive testing) technicians using ultrasonic testing, physics and materials science students, and anyone curious about how fast sound travels through different solids.
Regional Notes
Global: Material properties (Young's modulus, density) are universal constants from standard engineering references (ASTM, ASM International, and CRC Handbook). Values are at room temperature (20 °C / 68 °F) unless otherwise noted.
Frequently Asked Questions
What is the formula for the speed of sound in solids?
The speed of longitudinal (compression) waves in solids is v = √(E/ρ) where E is Young's modulus in pascals and ρ is the density in kg/m³. Shear wave speed is v = √(G/ρ) where G is the shear modulus. Sound travels faster in stiff, lightweight materials like diamond (12,000 m/s) and slower in dense, flexible materials like rubber (60 m/s).
Why does sound travel faster in solids than in air?
Sound travels faster in solids because solid materials have much higher stiffness (Young's modulus) compared to gases. While air has a bulk modulus of about 142 kPa, steel has a Young's modulus of 200 GPa — over a million times stiffer. The density also increases, but not by the same factor, so the net effect is a much higher wave speed.
What is the difference between longitudinal and shear waves in solids?
Longitudinal waves (P-waves) involve compression and rarefaction along the direction of travel, similar to sound in air. Shear waves (S-waves) involve perpendicular displacement and can only travel through solids because fluids cannot support shear stresses. P-waves always travel faster than S-waves in the same material — typically about 1.5 to 2 times faster.
How fast does sound travel in common solid materials?
Sound travels at approximately 5,960 m/s in steel, 6,420 m/s in aluminum, 4,760 m/s in copper, 5,010 m/s in titanium, 3,700 m/s in glass, 3,300 m/s in concrete, and 12,000 m/s in diamond. In soft materials like rubber, the speed drops to around 30-60 m/s.
How do you calculate the speed of sound in a solid?
Select a material from the dropdown (steel, aluminum, copper, etc.) and the calculator automatically uses the material's Young's modulus and density. For custom materials, enter your own values. The longitudinal speed is computed as v = √(E/ρ) where E is in Pa and ρ in kg/m³. The shear speed uses G = E/(2(1+ν)) with Poisson's ratio of 0.3.
Can I use custom material properties?
Yes, select 'Custom Material' from the dropdown or edit the Young's modulus or density fields directly. This allows you to calculate the speed of sound for any solid material by entering its Young's modulus in GPa and density in kg/m³. This is useful for novel materials, alloys, composites, or research-grade calculations.
Does temperature affect the speed of sound in solids?
Yes, temperature affects the speed of sound in solids, though less dramatically than in gases. As temperature increases, most materials expand (density decreases) and their Young's modulus decreases. The net effect for most metals is a small decrease in sound speed of about 0.03-0.07% per °C. This calculator uses room-temperature values.
What is Poisson's ratio and why is it used?
Poisson's ratio (ν) describes how a material deforms laterally when stretched longitudinally. For most metals, ν is approximately 0.3. It relates Young's modulus E to the shear modulus G via G = E/(2(1+ν)). This calculator assumes ν = 0.3, which gives a good approximation for common engineering materials like steel and aluminum.