Questions: What is the wavelength of a 60 mHz wave that travels at 400 m / s ? 1000 mHz=1 Hz

Transcript text: What is the wavelength of a 60 mHz wave that travels at $400 \mathrm{~m} / \mathrm{s}$ ? $1000 \mathrm{mHz}=1 \mathrm{~Hz}

Solution

Step 1: Convert Frequency to Hertz

First, we need to convert the frequency from millihertz (mHz) to hertz (Hz). Given that $1000 \, \text{mHz} = 1 \, \text{Hz}$:

\[ 60 \, \text{mHz} = \frac{60}{1000} \, \text{Hz} = 0.060 \, \text{Hz} \]

Step 2: Use the Wave Speed Formula

The relationship between the speed of a wave ($v$), its frequency ($f$), and its wavelength ($\lambda$) is given by the formula:

\[ v = f \lambda \]

Step 3: Solve for Wavelength

Rearrange the formula to solve for the wavelength ($\lambda$):

\[ \lambda = \frac{v}{f} \]

Substitute the given values ($v = 400 \, \text{m/s}$ and $f = 0.060 \, \text{Hz}$):

\[ \lambda = \frac{400 \, \text{m/s}}{0.060 \, \text{Hz}} = \frac{400}{0.060} \, \text{m} = 6666.6667 \, \text{m} \]

$\boxed{\lambda = 6666.6667 \, \text{m}}$

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