QuestionFind the wavelength of light in mm with a frequency of 645 MHz. Provide the answer in mm to 3 significant figures.

Studdy Solution

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 $1 \times10^3$ .
$\lambda =0.465 \, m \times1 \times10^3 =465 \, mm$

STEP 7

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.

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QuestionFind the wavelength of light in mm with a frequency of 645 MHz. Provide the answer in mm to 3 significant figures.

Studdy Solution

STEP 1

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 $1 \times10^3$ .
$\lambda =0.465 \, m \times1 \times10^3 =465 \, mm$

STEP 7

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.

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QuestionFind the wavelength of light in mm with a frequency of 645 MHz. Provide the answer in mm to 3 significant figures.

Studdy Solution

STEP 1

STEP 2

STEP 3

Now, we can use the wave equation to find the wavelength. Rearranging the equation to solve for λ\lambdaλ, we getλ=c/ν\lambda = c / \nuλ=c/ν

STEP 4

Plug in the values for the speed of light and the frequency to calculate the wavelength.λ=3.00×108 m/s/645×106 Hz\lambda =3.00 \times10^8 \, m/s /645 \times10^6 \, Hzλ=3.00×108m/s/645×106Hz

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 1×1031 \times10^31×103.λ=0.465 m×1×103=465 mm\lambda =0.465 \, m \times1 \times10^3 =465 \, mmλ=0.465m×1×103=465mm

STEP 7

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

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

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

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

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.