To solve for the wavelength ([tex]\(\lambda\)[/tex]) of the sound wave in water given its frequency ([tex]\(f\)[/tex]) and the speed of sound in water ([tex]\(v\)[/tex]), we can use the wave equation:
[tex]\[ v = f \times \lambda \][/tex]
We need to solve for the wavelength [tex]\(\lambda\)[/tex]. Rearranging the equation to solve for [tex]\(\lambda\)[/tex], we get:
[tex]\[ \lambda = \frac{v}{f} \][/tex]
Given:
- The frequency [tex]\(f\)[/tex] of the sound wave is 100 Hz.
- The speed of sound in water [tex]\(v\)[/tex] is 1493 m/s (from the table provided).
Substituting the given values into the equation, we have:
[tex]\[ \lambda = \frac{1493 \text{ m/s}}{100 \text{ Hz}} \][/tex]
[tex]\[ \lambda = 14.93 \text{ m} \][/tex]
Therefore, the wavelength of the sound wave in water is [tex]\( \boxed{14.93 \text{ m}} \)[/tex].
This corresponds to option C from the provided choices.
