In a medium, a longitudinal wave has speed $v$ and frequency $f$. What is the wavelength $\lambda$ of the wave?

• A. $\lambda =v+f$
• B. $\lambda =\frac{f}{v}$
• C. $\lambda =vf$
• D. $\lambda =\frac{v}{f}$

Answer: (D)

Verified step by step guidance

1. Recall the fundamental relationship between wave speed (v), frequency (f), and wavelength (\(\lambda\)) for any wave: the wave speed is equal to the product of its frequency and wavelength.
2. Express this relationship mathematically as: \(v = f \times \lambda\).
3. To find the wavelength (\(\lambda\)), rearrange the equation to solve for \(\lambda\) by dividing both sides by the frequency (f): \(\lambda = \frac{v}{f}\).
4. Interpret this result: the wavelength is the distance between successive wave crests and depends on how fast the wave travels and how frequently the crests pass a point.
5. Thus, given the wave speed and frequency, you can calculate the wavelength using the formula \(\lambda = \frac{v}{f}\).