To determine the wavelength of the wave in brass, we need to use the fundamental wave equation that relates wave speed, frequency, and wavelength. The relationship can be described by the formula:
[tex]\[ v = f \lambda \][/tex]
Where:
- [tex]\( v \)[/tex] is the wave speed in the medium (m/s),
- [tex]\( f \)[/tex] is the frequency of the wave (Hz),
- [tex]\( \lambda \)[/tex] is the wavelength of the wave (m).
In this problem, we are given:
- The frequency ([tex]\( f \)[/tex]) of the wave is [tex]\( 200 \)[/tex] Hz,
- The wave speed ([tex]\( v \)[/tex]) in brass is [tex]\( 4700 \)[/tex] m/s.
We are asked to find the wavelength ([tex]\( \lambda \)[/tex]) of the wave in brass. Rearranging the wave equation to solve for wavelength, we get:
[tex]\[ \lambda = \frac{v}{f} \][/tex]
Substituting the given values into the equation:
[tex]\[ \lambda = \frac{4700 \, \text{m/s}}{200 \, \text{Hz}} \][/tex]
[tex]\[ \lambda = 23.5 \, \text{m} \][/tex]
Therefore, the wavelength of the wave in brass is [tex]\( 23.5 \)[/tex] meters.
So, the correct answer is:
B. [tex]\( 23.5 \, \text{m} \)[/tex]
