How is wavelength calculated?

How is wavelength calculated?

• A. Frequency divided by velocity
• B. Velocity minus frequency
• C. Velocity divided by frequency
• D. Product of velocity and frequency

Answer: (C)

The wavelength is the distance the wave travels in one cycle. In a nondispersive medium, this is determined by the formula λ = v / f, where v is the wave speed in the material and f is the frequency. Since one cycle lasts 1/f seconds, the wave covers v times that duration, which is v/f meters—the wavelength. The units also line up: meters per second divided by cycles per second gives meters. If you tried the other options, you’d get the wrong type of quantity: frequency divided by velocity has units of 1/m (not a length), velocity minus frequency isn’t a meaningful length relation, and velocity times frequency would mix units and not equal a wavelength. For example, with v = 5000 m/s and f = 2,000,000 Hz, λ = 5000 / 2,000,000 = 0.0025 m (2.5 mm).

The wavelength is the distance the wave travels in one cycle. In a nondispersive medium, this is determined by the formula λ = v / f, where v is the wave speed in the material and f is the frequency. Since one cycle lasts 1/f seconds, the wave covers v times that duration, which is v/f meters—the wavelength. The units also line up: meters per second divided by cycles per second gives meters.

If you tried the other options, you’d get the wrong type of quantity: frequency divided by velocity has units of 1/m (not a length), velocity minus frequency isn’t a meaningful length relation, and velocity times frequency would mix units and not equal a wavelength. For example, with v = 5000 m/s and f = 2,000,000 Hz, λ = 5000 / 2,000,000 = 0.0025 m (2.5 mm).