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A sound wave traveling through dry air has a frequency of 16 Hz, a wavelength of 22 m, and a speed of [tex]350 \, \text{m/s}[/tex]. When the sound wave passes through a cloud of methane, its wavelength changes to 28 m, while its frequency remains the same. What is its new speed? (The equation for the speed of a wave is [tex]v = f \times \lambda[/tex].)

A. [tex]13 \, \text{m/s}[/tex]
B. [tex]9,800 \, \text{m/s}[/tex]
C. [tex]448 \, \text{m/s}[/tex]
D. [tex]350 \, \text{m/s}[/tex]



Answer :

GinnyAnswer
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]

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