Wave Speed Calculator
The speed of a wave (\(v\)) is determined by its frequency (\(f\)) and its wavelength (\(\lambda\)). This fundamental relationship is described by the wave equation:
$$ v = f \cdot \lambda $$
Where \(v\) is velocity (m/s), \(f\) is frequency (Hz), and \(\lambda\) is wavelength (m). This equation applies to all periodic waves, including sound, light, and seismic waves.
Tip: Enter any TWO parameters below. The third will be automatically calculated. Adjust the Amplitude to modify the visual wave height!
Primary Parameters
Visual Controls
Reference Speeds:
• Sound (Air, 20°C): 343 m/s
• Sound (Water): 1480 m/s
• Light (Vacuum): 299,792,458 m/s
• Sound (Air, 20°C): 343 m/s
• Sound (Water): 1480 m/s
• Light (Vacuum): 299,792,458 m/s
1. Wave Physics Dashboard
Solved Variable
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Period (\(T\))
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Angular Freq (\(\omega\))
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2. Dynamic Wave Simulation
Visualization of the wave. The oscillation frequency and spatial density (wavelength) are linked to your inputs.
3. Wavelength vs. Frequency Correlation
At a constant velocity, wavelength and frequency are inversely proportional.
4. Mathematical Derivation
Bernoulli Equation & Venturi Calculator
Fluid Energy Lab: Mastering Pressure, Velocity, and Elevation
Quick Answer
Bernoulli’s Equation is the principle of energy conservation for moving fluids. It states that the sum of Static Pressure, Dynamic Pressure, and Hydrostatic Pressure remains constant along a streamline. Our V4.0 engine solves for these variables by integrating the Continuity Equation (A₁v₁ = A₂v₂).
Table of Contents
1. The Ideal Bernoulli Formula
In a frictionless, incompressible fluid, the energy at any two points along a streamline is balanced as follows:
P1 + ½ρv12 + ρgz1 = P2 + ½ρv22 + ρgz2
2. Venturi Effect: Speed vs. Pressure
🌬️ The Dynamic Trade-off
The Venturi effect is the most famous application of Bernoulli. When fluid is forced through a narrowed pipe, its velocity increases. To maintain the energy balance, the static pressure must decrease. This creates the ‘suction’ used in carburetors and industrial aspirators.
3. Integrating the Continuity Equation
Our V4.0 engine automates the most tedious part of fluid math: calculating velocity from pipe dimensions. Based on the Continuity Principle, the mass flow rate remains constant throughout the system.
v2 = v1 × (D1 / D2)2
Simply enter your pipe diameters, and the solver automatically injects the resulting velocities into the Bernoulli equation.
4. Elevation (z) & Hydrostatic Head
Bernoulli is essential for civil engineering and plumbing. The ρgz term accounts for the potential energy of the fluid based on its height relative to a reference datum.
Head Pressure: In water systems, every 10 meters (33 ft) of vertical height adds approximately 1 bar (14.5 psi) of hydrostatic pressure to the bottom of the column.
5. Pressure Components Explained
- Static Pressure (P): The actual thermodynamic pressure of the fluid.
- Dynamic Pressure (½ρv²): The kinetic energy converted into pressure units.
- Hydrostatic Pressure (ρgz): The pressure exerted by the weight of the fluid column.
6. Assumptions & Validity Guard
🚨 The “Ideal” Limit
Bernoulli is an approximation. Our engine monitors your inputs and warns you if the assumptions are violated:
- Compressibility: For air, if Mach > 0.3, density is no longer constant.
- Viscosity: Bernoulli ignores friction. In long pipes, Head Loss will make real pressure lower than calculated.
- Heat Transfer: The process must be adiabatic for the energy balance to hold.
7. Fluid Dynamics FAQs
Why does pressure drop in a narrow pipe?
Because the fluid speeds up. Kinetic energy increases, and that energy must come from the static pressure’s potential energy.
Can Bernoulli be used for gas?
Yes, as long as the flow is low-speed (subsonic) and density changes are negligible.
8. Energy Conservation Takeaways
- 🏁 Total Energy: It is always conserved along a streamline.
- 🏁 Velocity-Pressure Inverse: High speed equals low pressure.
- 🏁 Elevation Impact: Height directly converts to static pressure.
- 🏁 Constraint: Always check for viscosity and compressibility in real-world apps.
Initialize Fluid Energy Solver
Run full Bernoulli and Continuity simulations with V4.0 accuracy.
Calculate Bernoulli Equation