To solve for the new speed of the sound wave when it passes through a cloud of methane, we can follow these steps:
1. Identify the given values:
- Frequency of the sound wave [tex]\( f \)[/tex] in both air and methane is [tex]\( 16 \)[/tex] Hz.
- Wavelength of the sound wave in methane [tex]\( \lambda_{methane} \)[/tex] is [tex]\( 28 \)[/tex] meters.
2. Understand the formula for the speed of a wave:
[tex]\[
v = f \times \lambda
\][/tex]
Where:
- [tex]\( v \)[/tex] is the speed of the wave.
- [tex]\( f \)[/tex] is the frequency.
- [tex]\( \lambda \)[/tex] is the wavelength.
3. Plug the values into the wave speed formula:
[tex]\[
v_{methane} = f \times \lambda_{methane}
\][/tex]
Substituting the given values:
[tex]\[
v_{methane} = 16 \, Hz \times 28 \, m
\][/tex]
4. Calculate the speed of the wave in methane:
[tex]\[
v_{methane} = 16 \times 28 = 448 \, m/s
\][/tex]
Based on these steps, the new speed of the sound wave through the methane is [tex]\(\mathbf{448 \, m/s}\)[/tex].
Thus, the correct answer is:
C. [tex]\(448 \, m/s\)[/tex]
