To determine which of the given options correctly defines the speed of a wave, let's start by understanding the fundamental relationship between the speed of a wave ([tex]\(v\)[/tex]), its frequency ([tex]\(f\)[/tex]), and its wavelength ([tex]\(\lambda\)[/tex]).
The speed of a wave is given by the product of its frequency and wavelength. This relationship can be expressed mathematically as:
[tex]\[ v = f \lambda \][/tex]
Here's a breakdown of each option provided:
Option A: [tex]\( v = \frac{f}{\lambda} \)[/tex]
- This expression implies that the speed of the wave is equal to the frequency divided by the wavelength, which is incorrect based on the fundamental wave equation.
Option B: [tex]\( \lambda = v f \)[/tex]
- This expression implies that the wavelength is equal to the speed of the wave times the frequency. This is a rearrangement of the wave equation but incorrectly places [tex]\( \lambda \)[/tex] as the product, which is not the standard form for defining the speed of a wave.
Option C: [tex]\( f = \nu \lambda \)[/tex]
- Here, the expression uses [tex]\(\nu\)[/tex] (often substituted with [tex]\(v\)[/tex] in place of wave speed), equating frequency times wavelength to frequency. This is inconsistent because it erroneously equates frequency to the product of frequency and wavelength.
Option D: [tex]\( v = f \lambda \)[/tex]
- This expression correctly states that the speed of the wave is the product of the frequency and wavelength of the wave. This is the standard and widely accepted form for defining the speed of a wave.
Therefore, the correct answer is:
[tex]\[ \boxed{D. \, v = f \lambda} \][/tex]
