Which equation relates speed, frequency, and wavelength?

Which equation relates speed, frequency, and wavelength?

• A. Speed = Frequency x Wavelength
• B. Speed = Wavelength / Frequency
• C. Speed = Frequency / Wavelength
• D. Speed = 1/(Frequency x Wavelength)

Answer: (A)

When a wave travels, speed is how far a crest moves each second. Each cycle spans a distance equal to the wavelength, and cycles occur f times per second, so the distance per second is f × λ. That makes the speed equal to the product of frequency and wavelength: v = f × λ. This fits because Hz is 1/s, so multiplying frequency by wavelength (meters) gives meters per second, the units of speed. The other forms don’t produce units of speed (for example, λ divided by f gives meters·seconds, not m/s; f divided by λ gives 1/(s·m); and 1/(fλ) gives s/m). In practice, for light in a vacuum, c = fλ, a constant; when light enters a different medium, frequency stays the same while speed and wavelength change so that v = fλ still holds.

When a wave travels, speed is how far a crest moves each second. Each cycle spans a distance equal to the wavelength, and cycles occur f times per second, so the distance per second is f × λ. That makes the speed equal to the product of frequency and wavelength: v = f × λ.

This fits because Hz is 1/s, so multiplying frequency by wavelength (meters) gives meters per second, the units of speed. The other forms don’t produce units of speed (for example, λ divided by f gives meters·seconds, not m/s; f divided by λ gives 1/(s·m); and 1/(fλ) gives s/m). In practice, for light in a vacuum, c = fλ, a constant; when light enters a different medium, frequency stays the same while speed and wavelength change so that v = fλ still holds.