To solve the problem of finding the wavelength of a sound wave in water given certain parameters, we can use the wave speed equation. The equation is:
[tex]\[ v = f \times \lambda \][/tex]
where:
- \( v \) is the speed of the sound wave in the medium (in this case, water),
- \( f \) is the frequency of the sound wave,
- \( \lambda \) is the wavelength of the sound wave.
Given data for water:
- The speed of sound in water \( v = 1493 \, \text{m/s} \)
- The frequency of the sound wave \( f = 20 \, \text{Hz} \)
We need to find the wavelength \( \lambda \). Rearrange the equation to solve for \( \lambda \):
[tex]\[ \lambda = \frac{v}{f} \][/tex]
Now, substituting the given values into the equation:
[tex]\[ \lambda = \frac{1493 \, \text{m/s}}{20 \, \text{Hz}} \][/tex]
After performing the division:
[tex]\[ \lambda = \frac{1493}{20} \][/tex]
[tex]\[ \lambda = 74.65 \, \text{m} \][/tex]
Thus, the wavelength of the sound wave in water is \( \lambda = 74.65 \, \text{m} \).
From the given options:
A. \( 54.3 \, \text{m} \)
B. \( 74.7 \, \text{m} \)
C. \( 64.5 \, \text{m} \)
D. \( 17.3 \, \text{m} \)
The closest matching option is \( 74.7 \, \text{m} \).
Therefore, the correct answer is:
[tex]\[ \boxed{74.7 \, \text{m}} \][/tex]
