To solve this problem, we need to determine the wavelength of the sound wave in water. The formula given for the speed of a wave is:
[tex]\[ v = f \times \lambda \][/tex]
where:
- [tex]\( v \)[/tex] is the speed of the sound wave,
- [tex]\( f \)[/tex] is the frequency of the sound wave,
- [tex]\( \lambda \)[/tex] is the wavelength of the sound wave.
We can solve for the wavelength [tex]\( \lambda \)[/tex]:
[tex]\[ \lambda = \frac{v}{f} \][/tex]
The problem provides the following information:
- The frequency of the sound wave [tex]\( f = 100 \, \text{Hz} \)[/tex],
- The speed of sound in water [tex]\( v = 1,493 \, \text{m/s} \)[/tex].
Substituting these values into the formula:
[tex]\[ \lambda = \frac{1,493 \, \text{m/s}}{100 \, \text{Hz}} \][/tex]
Perform the division:
[tex]\[ \lambda = 14.93 \, \text{m} \][/tex]
Therefore, the wavelength of the sound wave in water is 14.93 meters.
So, the correct answer is:
D. 14.93 m
