λ = v / f | Wave Speed, Frequency & Wavelength | Physics Tool for Sound, Light & EM Waves
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📝 Step-by-step solution
Select what to calculate and enter values
💡 Wavelength λ in meters | Wave speed v in m/s | Frequency f in Hertz (Hz = 1/s) | For light in vacuum, v = c = 3×10⁸ m/s | Sound in air ~ 343 m/s
📖 How to Use This Wavelength Calculator
1
Select what to calculate - Choose Wavelength (λ), Frequency (f), or Wave Speed (v).
2
Enter known values - Input the two known quantities based on the formula λ = v/f.
3
Click "Calculate" - Get the result with step-by-step solution.
📡 Understanding Wave Relationships
The fundamental wave equation is λ = v/f, where λ (lambda) is wavelength, v is wave speed, and f is frequency. This equation shows the inverse relationship between wavelength and frequency: higher frequency means shorter wavelength, and vice versa.
For electromagnetic waves in vacuum, v = c (speed of light = 299,792,458 m/s ≈ 3×10⁸ m/s). For sound in air at room temperature, v ≈ 343 m/s.
📊 Wave Properties Cheat Sheet
Radio waves: λ = 1 mm to 100 km | f = 3 kHz to 300 GHz
Microwaves: λ = 1 mm to 1 m | f = 300 MHz to 300 GHz
Infrared (IR): λ = 700 nm to 1 mm | f = 300 GHz to 430 THz
Ultraviolet (UV): λ = 10-400 nm | f = 750 THz to 30 PHz
X-rays: λ = 0.01-10 nm | f = 30 PHz to 30 EHz
Gamma rays: λ < 0.01 nm | f > 30 EHz
Sound (audible): λ = 0.017-17 m | f = 20 Hz - 20 kHz
🧮 Wavelength Formulas
Wavelength: λ = v / f Frequency: f = v / λ Wave Speed: v = λ × f
For light in vacuum: λ = c / f, where c = 3×10⁸ m/s
💡 Real-World Applications
Wireless Communication: Cell phones, Wi-Fi, radio use specific frequencies (and thus wavelengths)
Music & Audio: Musical notes correspond to specific frequencies; wavelength determines room acoustics
Medical Imaging: Ultrasound uses high-frequency sound waves
Optics: Lens design depends on light wavelengths
Astronomy: Redshift and blueshift use wavelength shifts to measure cosmic motion
❓ Frequently Asked Questions (FAQ)
What is the relationship between wavelength and frequency?
Wavelength and frequency are inversely proportional: λ = v/f. Higher frequency means shorter wavelength. For example, blue light has higher frequency and shorter wavelength than red light.
How do I convert frequency to wavelength for light?
Use λ = c / f, where c = 3×10⁸ m/s. For example, red light (f ≈ 4.3×10¹⁴ Hz) has λ = 3×10⁸ / 4.3×10¹⁴ ≈ 7×10⁻⁷ m = 700 nm.
What is the speed of sound in air?
At 20°C (68°F), the speed of sound is approximately 343 m/s (1,125 ft/s). It increases with temperature: v ≈ 331 + 0.6T m/s (T in °C).
What is the visible light spectrum range?
Visible light wavelengths range from about 400 nm (violet) to 700 nm (red). Frequency ranges from about 430 THz (red) to 750 THz (violet).
Why do different colors have different wavelengths?
Different colors correspond to different frequencies of light. The speed of light is constant in a medium, so wavelength varies inversely with frequency. Red has lowest frequency/longest wavelength; violet has highest frequency/shortest wavelength.
How does wavelength affect diffraction?
Waves diffract (bend) around obstacles. Longer wavelengths diffract more than shorter wavelengths. This is why radio waves (long λ) bend around buildings, but light (short λ) does not.