Which equation correctly expresses wavelength in terms of propagation speed and frequency?

Which equation correctly expresses wavelength in terms of propagation speed and frequency?

• A. Wavelength = Speed × Frequency
• B. Wavelength = Speed / Frequency
• C. Wavelength = Frequency / Speed
• D. Wavelength = 1 / Speed

Answer: (B)

The key relationship here is that a wave’s speed equals its frequency times its wavelength. Therefore, the wavelength is the speed divided by the frequency. This makes sense with units: meters per second divided by cycles per second gives meters. If you keep speed fixed and raise the frequency, the wavelength must shrink. For example, light travels about 3.0×10^8 m/s; at 6.0×10^14 Hz, the wavelength is roughly 5.0×10^-7 m (500 nm). The other forms don’t yield a length with the correct units: multiplying speed by frequency would give something like m/s^2, dividing frequency by speed gives 1/m, and taking the reciprocal of speed gives seconds per meter.

The key relationship here is that a wave’s speed equals its frequency times its wavelength. Therefore, the wavelength is the speed divided by the frequency. This makes sense with units: meters per second divided by cycles per second gives meters. If you keep speed fixed and raise the frequency, the wavelength must shrink. For example, light travels about 3.0×10^8 m/s; at 6.0×10^14 Hz, the wavelength is roughly 5.0×10^-7 m (500 nm). The other forms don’t yield a length with the correct units: multiplying speed by frequency would give something like m/s^2, dividing frequency by speed gives 1/m, and taking the reciprocal of speed gives seconds per meter.