Wave Calculator
Choose a mode. Enter known values. Select the unknown result.
Live Wave Visualization
Formula Used
v = f × λf = v ÷ λλ = v ÷ fT = 1 ÷ fω = 2πfk = 2π ÷ λv string = √(F ÷ μ)v shallow = √(g × d)c material = c ÷ n
Variable Definitions
v means wave speed.
f means frequency.
λ means wavelength.
T means period.
ω means angular frequency.
k means wave number.
How to Use This Calculator
- Select a calculation mode.
- Choose the value needing calculation.
- Enter all known measurements.
- Select matching units carefully.
- Choose result precision.
- Press the calculate button.
- Review formulas and converted results.
- Export results when needed.
Example Data Table
| Wave type | Speed | Frequency | Wavelength |
|---|---|---|---|
| Audible sound in air | 343 m/s | 1,000 Hz | 0.343 m |
| Low bass sound | 343 m/s | 50 Hz | 6.86 m |
| Ultrasound scanner | 1,540 m/s | 5,000,000 Hz | 0.000308 m |
| FM radio | 299,792,458 m/s | 100,000,000 Hz | 2.99792458 m |
| Wi-Fi 2.4 GHz | 299,792,458 m/s | 2.40000000e+9 Hz | 0.12491352 m |
| Microwave oven | 299,792,458 m/s | 2.45000000e+9 Hz | 0.12236427 m |
| Red light | 299,792,458 m/s | 4.62000000e+14 Hz | 6.49000000e-7 m |
| Green light | 299,792,458 m/s | 5.50000000e+14 Hz | 5.45000000e-7 m |
| Blue light | 299,792,458 m/s | 6.67000000e+14 Hz | 4.50000000e-7 m |
| Ultraviolet | 299,792,458 m/s | 1.00000000e+15 Hz | 2.99790000e-7 m |
| X-ray example | 299,792,458 m/s | 3.00000000e+18 Hz | 9.99300000e-11 m |
| Gamma ray example | 299,792,458 m/s | 3.00000000e+20 Hz | 9.99300000e-13 m |
| Ocean swell | 15.6 m/s | 0.1 Hz | 156 m |
| Seismic P-wave | 6,000 m/s | 5 Hz | 1,200 m |
| Seismic S-wave | 3,500 m/s | 5 Hz | 700 m |
Common Wave Speeds
| Medium | Approximate speed | Context |
|---|---|---|
| Air at 0°C | 331.3 m/s | Approximate sound speed |
| Air at 20°C | 343 m/s | Approximate sound speed |
| Helium | 1,007 m/s | Approximate sound speed |
| Fresh water | 1,481 m/s | Approximate sound speed |
| Seawater | 1,531 m/s | Approximate sound speed |
| Concrete | 3,200 m/s | Material dependent |
| Glass | 4,540 m/s | Material dependent |
| Steel | 5,960 m/s | Longitudinal estimate |
| Aluminum | 6,320 m/s | Longitudinal estimate |
| Vacuum | 299,792,458 m/s | Electromagnetic waves |
Understanding Wave Relationships
Wave speed connects space and time
Every repeating wave has a frequency. Every wave also has wavelength. Their product gives wave speed. Higher frequency shortens wavelength when speed remains fixed. Lower frequency lengthens wavelength under identical conditions.
Media change speed differently
Sound needs matter for propagation. Its speed depends on material properties. Temperature changes sound speed in air. Humidity creates smaller changes. Electromagnetic waves can cross a vacuum. Their vacuum speed is physically fixed. Materials reduce that speed through refractive behavior.
Frequency often remains unchanged
A wave crossing boundaries usually keeps frequency. The source controls that frequency. Speed can change inside another medium. Wavelength then changes with speed. This behavior explains refraction and many optical effects.
Period measures cycle duration
Period is frequency's reciprocal. High frequencies have very short periods. Low frequencies have longer periods. Angular frequency expresses cycling using radians. Wave number expresses spatial cycling using radians per meter.
String waves depend on tension
Tighter strings usually carry faster waves. Greater linear density slows wave motion. Length controls resonant frequencies. Harmonics appear at integer fundamental multiples. These ideas support musical instrument design.
Water waves need suitable models
Shallow waves strongly feel the seabed. Their speed depends mostly on depth. Deep waves behave differently. Their period helps estimate wavelength and speed. Real oceans can require dispersion equations.
Units require careful attention
Convert every input before applying formulas. Frequency should use cycles per second. Wavelength should use consistent distance units. Speed then follows matching distance units. Scientific notation helps extremely large frequencies. It also helps extremely small wavelengths.
Results remain approximations
Preset values represent typical conditions. Actual materials vary with temperature and composition. Pressure can affect gas behavior. Water salinity changes sound speed. Engineering work needs measured local values. Educational examples can use standard references.
Wave Glossary
| Term | Meaning |
|---|---|
| Amplitude | Maximum displacement from equilibrium. |
| Crest | Highest point on a transverse wave. |
| Cycle | One complete repeating wave pattern. |
| Dispersion | Frequency-dependent wave speed in a medium. |
| Frequency | Number of completed cycles each second. |
| Group velocity | Speed carrying wave energy or information. |
| Harmonic | Frequency equal to an integer fundamental multiple. |
| Longitudinal wave | Oscillation occurs parallel to travel direction. |
| Node | Standing-wave point with minimal displacement. |
| Period | Time required for one complete cycle. |
| Phase | Position within a repeating oscillation. |
| Phase velocity | Speed of a constant phase point. |
| Standing wave | Pattern created by opposing matching waves. |
| Transverse wave | Oscillation occurs perpendicular to travel direction. |
| Wave number | Spatial angular frequency measured in radians per meter. |
| Wavelength | Distance between matching points on adjacent cycles. |
Saved Calculation History
Saved results appear here.
Frequently Asked Questions
What equation connects wave speed, frequency, and wavelength?
Wave speed equals frequency multiplied by wavelength.
Can the calculator solve any missing variable?
Yes. Select the desired result and enter required values.
Why must frequency remain positive?
Zero frequency describes no repeating oscillation.
Does wavelength change inside another medium?
Yes. Frequency stays constant while speed and wavelength change.
What speed should electromagnetic waves use?
Use light speed divided by the material refractive index.
How does air temperature affect sound speed?
Warmer air generally increases the speed of sound.
What is angular frequency?
Angular frequency measures radians completed during each second.
What is wave number?
Wave number measures spatial phase change per meter.
Can this calculator handle string waves?
Yes. Enter tension and linear mass density.
Can it estimate shallow-water wave speed?
Yes. Enter water depth and local gravity.
Are preset material speeds exact?
No. Real speeds vary with composition and conditions.