Math Snap

STEP 1

Assumptions1. The frequency of the light is645 MHz. We are asked to find the wavelength in mm3. We are using the speed of light in vacuum, which is approximately $3.00 \times10^8$ m/s4. We are using the wave equation $c = \lambda \nu$, where $c$ is the speed of light, $\lambda$ is the wavelength, and $\nu$ is the frequency

STEP 2

First, we need to convert the frequency from MHz to Hz, because the speed of light is in m/s and we want the wavelength in meters initially. We can do this by multiplying the frequency by $1 \times10^6$.
$$\nu =645 \, MHz \times1 \times10^6 =645 \times10^6 \, Hz$$

STEP 3

Now, we can use the wave equation to find the wavelength. Rearranging the equation to solve for $\lambda$, we get$$\lambda = c / \nu$$

STEP 4

Plug in the values for the speed of light and the frequency to calculate the wavelength.
$$\lambda =3.00 \times10^8 \, m/s /645 \times10^6 \, Hz$$

STEP 5

Calculate the wavelength in meters.
\lambda =3.00 \times10^8 \, m/s /645 \times10^ \, Hz =0.465 \, m

STEP 6

Now, we need to convert the wavelength from meters to millimeters. We can do this by multiplying the wavelength by $1 \times10^3$.
$$\lambda =0.465 \, m \times1 \times10^3 =465 \, mm$$

Finally, we round the wavelength to three significant figures.
$$\lambda =465 \, mm =465 \, mm$$The wavelength of light with a frequency of645 MHz is465 mm.