What is the Wave Equation?
The wave equation connects a wave's speed to its frequency and wavelength. It applies to every type of wave — sound, water, light and more — and is one of the most widely used formulas in physics.
The wave equation states that a wave's speed equals its frequency times its wavelength: v = fλ, where f is in hertz and λ is in metres.
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Step-by-step worked examples
A sound wave has a frequency of 440 Hz (musical note A) and a wavelength of 0.78 m. Find its speed.
v = fλ v = 440 × 0.78 v = 343.2 m/s
A water wave has a wavelength of 3 m and travels at 6 m/s. Find its frequency.
v = fλ → f = v/λ f = 6/3 f = 2 Hz
Visible light has a frequency of 5×10¹⁴ Hz and a wavelength of 600 nm (6×10⁻⁷ m). Find its speed.
v = fλ v = (5×10¹⁴) × (6×10⁻⁷) v = 3×10⁸ m/s
Flashcards
Quick quiz
Q1.A wave has f = 20 Hz and λ = 0.5 m. Find v.
Q2.If wave speed stays constant and frequency doubles, wavelength:
Q3.What is the unit of frequency in the wave equation?
Q4.A radio wave has λ = 3 m and travels at 3×10⁸ m/s. Find its frequency.
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Common mistakes
Wave speed always depends on frequency. — Correct: In a fixed medium, wave speed is usually constant; frequency and wavelength adjust to keep v = fλ true.
Wavelength and frequency are directly proportional. — Correct: For constant speed, they're inversely proportional — higher f means shorter λ.
The wave equation only applies to sound. — Correct: v = fλ applies to all waves: sound, water, light, radio, and more.
Frequency is measured in metres. — Correct: Frequency is measured in hertz (Hz), which is cycles per second; wavelength is measured in metres.
FAQ
What is the formula for the wave equation?
v = fλ, where v is wave speed (m/s), f is frequency (Hz), and λ is wavelength (m).
What is the wave equation in physics?
It's the relationship v = fλ linking a wave's speed to how often it cycles (frequency) and how long each cycle is (wavelength).
How do you calculate wave speed from frequency and wavelength?
Multiply them: v = f × λ. Make sure frequency is in Hz and wavelength is in metres.
What are examples of the wave equation in real life?
Sound (v ≈ 343 m/s in air), light (v = 3×10⁸ m/s), and radio waves all follow v = fλ.