To determine the wavelength of the sound wave in water, we will use the given wave speed equation:
[tex]\[ v = f \times \lambda \][/tex]
Here:
- [tex]\(v\)[/tex] is the speed of sound in water.
- [tex]\(f\)[/tex] is the frequency of the sound wave.
- [tex]\(\lambda\)[/tex] is the wavelength of the sound wave.
From the problem statement, we know:
- The frequency [tex]\(f\)[/tex] of the sound wave is [tex]\(20 \, \text{Hz}\)[/tex].
- The speed of sound [tex]\(v\)[/tex] in water is [tex]\(1,493 \, \text{m/s}\)[/tex].
We need to solve for the wavelength [tex]\(\lambda\)[/tex]. Rearranging the equation [tex]\( v = f \times \lambda \)[/tex] to solve for [tex]\(\lambda\)[/tex], we get:
[tex]\[ \lambda = \frac{v}{f} \][/tex]
Substituting the known values:
[tex]\[ \lambda = \frac{1493 \, \text{m/s}}{20 \, \text{Hz}} \][/tex]
Calculating the value:
[tex]\[ \lambda = 74.65 \, \text{m} \][/tex]
So, the wavelength of the sound wave in water is approximately [tex]\(74.65 \, \text{m}\)[/tex].
Among the given options, the closest value to [tex]\(74.65 \, \text{m}\)[/tex] is:
[tex]\[ \boxed{74.7 \, \text{m}} \][/tex]
Thus, the correct answer is option:
A. [tex]\(74.7 \, \text{m}\)[/tex]
