State the relation among speed v, frequency f, and wavelength λ for a wave.

• A. v = f/λ
• B. v = λ f^2
• C. v = f λ
• D. v = λ/f

Answer: (C)

When a wave travels, the speed is how far a wave pattern moves per unit time. Each cycle spans a distance equal to the wavelength, and cycles pass a point at a rate given by the frequency. So in one second, f cycles pass, each spanning λ meters, giving a total distance v = fλ. The units work out: frequency is in s−1 and wavelength in meters, so their product is meters per second, the wave speed.

The other forms don’t match the units or the physical meaning: for example, f/λ has units of s−1 per meter, not speed; λf^2 has units of meters per second squared, which isn’t a speed; and λ/f would have units of meters times seconds, also not a speed. So the correct relation is v = fλ.