Suppose two waves are traveling at the same speed, but one has a shorter $\mathrm{wavelength}$ than the other. Which wave has the higher $\mathrm{frequency}$?

• A. Frequency does not depend on wavelength or speed.
• B. The wave with the longer wavelength has the higher frequency because $f=v\times \lambda$.
• C. Both waves have the same frequency since they travel at the same speed.
• D. The wave with the shorter wavelength has the higher frequency because $f=\frac{v}{\lambda }$.

Answer: (D)

Verified step by step guidance

1. Recall the fundamental relationship between wave speed (v), frequency (f), and wavelength (\( \lambda \)) given by the equation: \[ f = \frac{v}{\lambda} \]
2. Since both waves travel at the same speed (\( v \)), the frequency depends inversely on the wavelength (\( \lambda \)).
3. Identify that if one wave has a shorter wavelength, then its wavelength \( \lambda \) is smaller compared to the other wave.
4. Using the formula, a smaller wavelength \( \lambda \) in the denominator means the frequency \( f \) will be larger for the wave with the shorter wavelength.
5. Therefore, the wave with the shorter wavelength has the higher frequency because frequency and wavelength are inversely proportional when speed is constant.