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Speed of Sound in a Solid — result sheet
Estimate longitudinal sound speed in a solid from Young's modulus and density, then calculate travel time over a path.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For the simple longitudinal approximation, v = √(E/ρ); travel time = distance/v.
A longitudinal elastic wave in a solid travels faster when the material is stiffer and slower when it is denser. This first-order calculator uses Young's modulus divided by density, then turns the speed into a one-way transit time for the entered path.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Young's modulus — GPa; minimum 1.0E-6; maximum 1000000
- Material density — kg/m³; minimum 1.0E-6; maximum 1000000
- Travel path — m; minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Young's modulus | 200 |
| Material density | 7850 |
| Travel path | 10 |
A steel-like material gives about 5,048 m/s and a 10 m one-way travel time of about 1.981 ms.
Assumptions and limits
- The material behaves as a homogeneous, isotropic, linear elastic solid and the wave is treated as a simple longitudinal wave.
- Young's modulus is converted from GPa to Pa and density is in kg/m³.
- Poisson effects, shear waves, anisotropy, temperature, dispersion, attenuation, joints, and boundary reflections are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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