To determine the correct relationship between frequency, velocity, and wavelength, let's consider the known equation for wave motion.
The frequency [tex]\( f \)[/tex] of a wave is related to its velocity [tex]\( V \)[/tex] and its wavelength [tex]\( \lambda \)[/tex] by the equation:
[tex]\[ f = \frac{V}{\lambda} \][/tex]
This equation indicates that the frequency is equal to the velocity of the wave divided by its wavelength.
Now let's evaluate the given options:
- Option A: [tex]\( f = \frac{V}{\lambda} \)[/tex]. This matches the correct relationship where frequency is the ratio of velocity to wavelength.
- Option B: [tex]\( f = V + \lambda \)[/tex]. This would imply the frequency is the sum of the velocity and the wavelength, which is incorrect.
- Option C: [tex]\( f = \frac{\lambda}{V} \)[/tex]. This suggests that frequency is the ratio of wavelength to velocity, which is the inverse of the correct relationship.
- Option D: [tex]\( f = V \times \lambda \)[/tex]. This implies frequency is the product of velocity and wavelength, which is incorrect.
The correct equation that shows how frequency is related to velocity and wavelength is:
[tex]\[ \boxed{A. \; f = \frac{V}{\lambda}} \][/tex]
