Speed of Sound in Solids Calculator
Calculate sound speed in solid materials
For steel: ~200 GPa = 200×10⁹ Pa
For steel: ~7850 kg/m³
How to Use This Calculator
Select Material (Optional)
Choose a material from the dropdown to automatically fill Young's modulus and density values. Or select "Custom" to enter values manually.
Enter Young's Modulus
Input Young's modulus (E) in Pascals. This measures the material's stiffness. For steel, use ~200×10⁹ Pa.
Enter Density
Input the material density (ρ) in kg/m³. This measures the material's mass per unit volume.
Calculate
Click calculate to get the speed of sound: c = √(E / ρ).
Formula
c = √(E / ρ)
where c = speed of sound (m/s), E = Young's modulus (Pa), ρ = density (kg/m³)
Example (Steel):
E = 200×10⁹ Pa, ρ = 7850 kg/m³
c = √(200×10⁹ / 7850) = √(25,477,707) ≈ 5,048 m/s
Sound travels about 14.7 times faster in steel than in air at 20°C.
Note: This formula applies to longitudinal waves in rods. For bulk materials, the formula is more complex and depends on Poisson's ratio. The speed is typically 15-20% higher in bulk materials than in rods.
About Speed of Sound in Solids Calculator
The Speed of Sound in Solids Calculator determines the speed at which sound waves travel through solid materials based on Young's modulus and density. Sound travels much faster in solids than in gases or liquids due to the strong atomic bonds and high stiffness of solid materials.
When to Use This Calculator
- Materials Science: Characterize acoustic properties of materials
- Engineering: Design systems using sound propagation in solids
- Ultrasonics: Calculate sound speeds for ultrasonic testing
- Seismology: Understand seismic wave speeds in Earth's crust
- Physics Education: Learn about wave propagation in solids
- NDT Testing: Non-destructive testing using ultrasonic waves
Why Use Our Calculator?
- ✅ Quick Calculations: Get speed of sound instantly
- ✅ Material Database: Pre-filled values for common materials
- ✅ Accurate Results: Uses standard material physics formula
- ✅ Custom Materials: Enter properties for any material
- ✅ Free Tool: No registration required
Understanding Speed of Sound in Solids
Sound speed in solids depends on the material's elastic modulus (stiffness) and density. Stiffer, less dense materials transmit sound faster. The relationship c = √(E/ρ) shows that speed increases with stiffness and decreases with density.
- Sound is much faster in solids (1000-6000 m/s) than in air (~343 m/s)
- Stiffer materials (higher E) transmit sound faster
- Less dense materials (lower ρ) transmit sound faster
- Different wave types (longitudinal vs. transverse) have different speeds
- Speed varies with temperature and material structure
Typical Speeds of Sound in Solids
- Steel: ~5,000-6,000 m/s
- Aluminum: ~5,100 m/s
- Copper: ~3,500 m/s
- Glass: ~5,200 m/s
- Concrete: ~3,200 m/s
- Wood (along grain): ~3,300-5,000 m/s
Frequently Asked Questions
Why does sound travel faster in solids?
Sound travels faster in solids because atoms are closely packed and strongly bonded, making the material very stiff (high Young's modulus). The speed of sound is proportional to √(stiffness/density), and solids have much higher stiffness than gases or liquids.
What is Young's modulus?
Young's modulus (E) is a measure of a material's stiffness or resistance to deformation. It's defined as stress divided by strain and measured in Pascals (Pa). Higher values mean stiffer materials.
Does this formula work for all solids?
The formula c = √(E/ρ) applies to longitudinal waves in rods. For bulk materials, the speed is slightly higher and depends on Poisson's ratio. The formula is accurate for most engineering applications.
How does temperature affect speed in solids?
Temperature affects both Young's modulus and density. Generally, as temperature increases, modulus decreases and speed decreases slightly. However, the effect is smaller than in gases.
What are the fastest sound speeds in solids?
Diamond has one of the fastest sound speeds at ~12,000 m/s due to its extremely high stiffness. Other very fast materials include beryllium (~12,900 m/s) and certain crystalline materials with strong atomic bonds.