🎓 Physics • Waves
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Wave Speed Calculator (v = f·λ)
Solves wave speed v = f × λ with presets for sound in air, light in vacuum, and sound in water.
Universal Wave Mechanics Calculator
Calculate speed, frequency, period, and wavelength via v = f · λ.
Wave Presets:
Sinusoidal Wave ProfilePeriod T = 2.27 ms
Wavelength (λ)
0.7795 m
Period (T = 1/f)2.273 ms
Angular Freq (ω)2764.6 rad/s
Wavenumber (k)8.06 rad/m
Speed (km/h)1234.8 km/h
Step-by-Step Derivation
1. Wave Equation: λ = v / f
2. Substitution: λ = (343 m/s) / (440 Hz)
3. Wavelength: λ = 0.7795 meters (77.95 cm)
4. Period: T = 1 / f = 1 / 440 = 2.273 ms
5. Angular Frequency: ω = 2πf = 2764.60 rad/s | Wave Number: k = 2π/λ = 8.06 rad/m
What is the Wave Equation?
The fundamental wave equation connects velocity, frequency, and wavelength for all periodic waves.
Formula & Step-by-Step Calculation
v = f × λ
Velocity equals frequency times wavelength.
Worked Step-by-Step Examples
Example 1
Sound wave of 440 Hz in air (v = 343 m/s)
Solution: λ = 0.78 meters
• 343 / 440 ≈ 0.78 m
Common Real-World & Academic Use Cases
- ✓ Acoustic instrument tuning
- ✓ Radio transmission antenna sizing
- ✓ Sonar underwater ranging
How to Use the Wave Speed Calculator (v = f·λ)
1
Input Speed & Frequency
Enter m/s and Hz.
2
Inspect Wavelength
Review calculated wavelength and period.
Frequently Asked Questions
Q: What is the speed of light in vacuum?
Exactly 299,792,458 m/s (c ≈ 3 × 10⁸ m/s).