To determine the wavelength of the sound wave in water, we use the wave equation:
[tex]\[ v = f \times \lambda \][/tex]
Here:
- [tex]\( v \)[/tex] is the speed of sound in the medium (in this case, water).
- [tex]\( f \)[/tex] is the frequency of the wave.
- [tex]\( \lambda \)[/tex] is the wavelength of the wave.
We need to find [tex]\(\lambda\)[/tex], so we rearrange the equation to solve for [tex]\(\lambda\)[/tex]:
[tex]\[ \lambda = \frac{v}{f} \][/tex]
Given:
- The speed of sound in water ([tex]\( v \)[/tex]) is 1,493 m/s.
- The frequency of the sound wave ([tex]\( f \)[/tex]) is 20 Hz.
Substituting these values into the equation:
[tex]\[ \lambda = \frac{1493 \, \text{m/s}}{20 \, \text{Hz}} \][/tex]
[tex]\[ \lambda = 74.65 \, \text{m} \][/tex]
Therefore, the wavelength of the sound wave in water is [tex]\( 74.65 \, \text{m} \)[/tex].
Given the options:
A. 64.5 m
B. 17.3 m
C. 74.7 m
D. 54.3 m
The closest match to our calculated wavelength is option C.
Thus, the correct answer is C. 74.7 m.
