recall and use v = f λ

Progressive Waves

What is a Progressive Wave?

Imagine a stone dropped in a calm pond. The ripples that move outward are a progressive wave – the disturbance travels through the medium while the particles of the medium only oscillate locally. 🌊

Key Relationship: 𝑣 = 𝑓 λ

𝑣 – speed of the wave (m s⁻¹) 𝑓 – frequency (Hz) λ – wavelength (m) The product of frequency and wavelength gives the speed at which the wavefront moves. 📐

Analogy: The Wave Train

Think of a line of people holding hands and marching forward. Each person moves up and down (oscillation) but the line itself moves forward (wave propagation). The speed of the line is analogous to 𝑣, the number of people passing a point per second is 𝑓, and the distance between successive people is λ. 🚶‍♂️🚶‍♀️

Worked Example 1 – Sound in Air

Given: 𝑣 = 343 m s⁻¹, 𝑓 = 500 Hz Find λ.
λ = 𝑣 / 𝑓 = 343 m s⁻¹ ÷ 500 Hz = 0.686 m
So the wavelength is about 0.69 m. 🎶

Worked Example 2 – Light in Vacuum

Given: 𝑣 = 3.00 × 10⁸ m s⁻¹, 𝑓 = 5.0 × 10¹⁴ Hz λ = 𝑣 / 𝑓 = (3.00 × 10⁸) ÷ (5.0 × 10¹⁴) = 6.0 × 10⁻⁷ m = 600 nm
That’s orange light! 🌈

Common Wave Speeds

Examination Tips

1️⃣ Check Units – speed in m s⁻¹, frequency in Hz, wavelength in m.
2️⃣ Use the Correct Formula – 𝑣 = 𝑓 λ or λ = 𝑣 / 𝑓.
3️⃣ Convert Units if Needed – e.g., mm to m, kHz to Hz.
4️⃣ Think About the Medium – Speed changes with medium; remember typical values.
5️⃣ Show All Work – Even if you’re confident, write the steps; marks are awarded for clarity.
Good luck! 🎓