What is the relationship between wave speed v, wavelength λ, and frequency f?

What is the relationship between wave speed v, wavelength λ, and frequency f?

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

Answer: (B)

Think about what speed means for a wave: how far a crest travels in one second. The frequency tells you how many crests pass a point each second, and the wavelength tells you how far apart successive crests are. Put those ideas together and you get v = f × λ. In one second, f crests pass by, and each crest spans a distance λ, so the total distance traveled is f times λ. This also matches units: f is in s⁻¹ and λ is in meters, giving v in meters per second. Because of this relationship, if the speed in a medium is fixed, increasing the frequency must decrease the wavelength proportionally, and vice versa. The other forms don’t line up with how speed, frequency, and wavelength interact; their units don’t match speed, so they don’t represent the correct relationship.

Think about what speed means for a wave: how far a crest travels in one second. The frequency tells you how many crests pass a point each second, and the wavelength tells you how far apart successive crests are. Put those ideas together and you get v = f × λ. In one second, f crests pass by, and each crest spans a distance λ, so the total distance traveled is f times λ. This also matches units: f is in s⁻¹ and λ is in meters, giving v in meters per second.

Because of this relationship, if the speed in a medium is fixed, increasing the frequency must decrease the wavelength proportionally, and vice versa. The other forms don’t line up with how speed, frequency, and wavelength interact; their units don’t match speed, so they don’t represent the correct relationship.