f = v/λ | v = fλ | T = 1/f | Wave speed, wavelength, period | Physics Tool
Result
--
📝 Step-by-step solution
Select calculation type and enter values
💡 Frequency f (Hz) | Wavelength λ (m) | Wave speed v (m/s) | Period T (s) | v = f·λ, T = 1/f | Light in vacuum: v = 3×10⁸ m/s
📖 How to Use This Frequency Calculator
1
Select what you want to calculate - Frequency (f), Wavelength (λ), Wave Speed (v), or Period (T).
2
Enter the known values - For frequency: wave speed and wavelength. For wavelength: wave speed and frequency. For wave speed: frequency and wavelength. For period: frequency.
3
Click "Calculate" - Get your result with a complete step-by-step solution.
📡 Understanding Wave Properties
Frequency (f) is the number of wave cycles that pass a fixed point per second, measured in Hertz (Hz). Wavelength (λ) is the distance between consecutive wave crests (meters). Wave speed (v) is how fast the wave travels (m/s). Period (T) is the time for one complete cycle (seconds), related by T = 1/f.
The wave equation is fundamental: v = f × λ (wave speed = frequency × wavelength). This applies to all types of waves: sound, light, water, and electromagnetic waves.
📊 Wave Formulas
Frequency: f = v / λ Wavelength: λ = v / f Wave Speed: v = f × λ Period: T = 1 / f
In electromagnetic waves: v = c = 3 × 10⁸ m/s (speed of light in vacuum)
🔬 Real-World Wave Examples
Sound Waves: Speed ≈ 343 m/s in air. Human hearing: 20 Hz - 20,000 Hz
Radio Waves: FM radio: 88-108 MHz, wavelength ≈ 3 meters
Earthquakes (P-waves): Speed ~ 5-8 km/s through rock
Water Waves: Speed depends on depth and gravity
💡 The Electromagnetic Spectrum
Radio Waves: f = 3 kHz - 300 GHz, λ = 1 mm - 100 km
Microwaves: f = 300 MHz - 300 GHz, λ = 1 mm - 1 m
Infrared: f = 300 GHz - 430 THz, λ = 700 nm - 1 mm
Visible Light: f = 430-750 THz, λ = 400-700 nm
Ultraviolet: f = 750 THz - 30 PHz, λ = 10-400 nm
X-rays: f = 30 PHz - 30 EHz, λ = 0.01-10 nm
Gamma Rays: f > 30 EHz, λ < 0.01 nm
❓ Frequently Asked Questions (FAQ)
What is the relationship between frequency and wavelength?
Frequency and wavelength are inversely proportional. As frequency increases, wavelength decreases (for constant wave speed). This is why higher frequency waves (like UV light) have shorter wavelengths than lower frequency waves (like radio waves).
What is the speed of light in different media?
Light speed in vacuum: c = 299,792,458 m/s ≈ 3×10⁸ m/s. In water: ~225,000,000 m/s (75% of c). In glass: ~200,000,000 m/s (67% of c). This causes refraction.
How does temperature affect sound speed?
Sound speed in air increases with temperature: v ≈ 331 + 0.6×T (m/s), where T is temperature in °C. At 0°C: 331 m/s, at 20°C: 343 m/s, at 30°C: 349 m/s.
What is the Doppler effect?
The Doppler effect is the change in frequency perceived when a wave source moves relative to an observer. Approaching source = higher frequency (higher pitch); receding = lower frequency. Used in radar, ultrasound, and astronomy.
What is the difference between transverse and longitudinal waves?
Transverse waves (light, water) oscillate perpendicular to direction of travel. Longitudinal waves (sound, P-waves) oscillate parallel to direction of travel (compressions and rarefactions).
Why is period the reciprocal of frequency?
If frequency is cycles per second, period is seconds per cycle. They are mathematical inverses: T = 1/f. For example, 60 Hz AC power has period T = 1/60 ≈ 0.0167 seconds.