Question #0a254

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Question #0a254

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Answer 1 · 2017-04-24T17:03:07

Please see the explanation.

Explanation:

The wavelength of $550 kHz$ $550" kHz"$ is:

$\frac{3.0 \times 10^{8} m/s}{5.5 \times 10^{5} Hz} = 545.5 m$ $(3.0xx10^8" m/s")/(5.5xx10^5" Hz")= 545.5" m"$

The wavelength of $1600 kHz$ $1600" kHz"$ is:

$\frac{3.0 \times 10^{8} m/s}{1.6 \times 10^{6} Hz} = 187.5 m$ $(3.0xx10^8" m/s")/(1.6xx10^6" Hz")= 187.5" m"$

The wavelength of 88 MHz is:

$\frac{3.0 \times 10^{8} m/s}{8.8 \times 10^{7} Hz} = 3.4 m$ $(3.0xx10^8" m/s")/(8.8xx10^7" Hz")= 3.4" m"$

The wavelength of 108 MHz is:

$\frac{3.0 \times 10^{8} m/s}{1.08 \times 10^{8} Hz} = 2.8 m$ $(3.0xx10^8" m/s")/(1.08xx10^8" Hz")= 2.8" m"$

Answer 2 · 2017-04-24T17:27:38

AM signals: $188 m - 545 m$ $188"m"-545"m"$
FM signals: $2.8 m - 3.4 m$ $2.8"m"-3.4"m"$

Explanation:

From the chemistry reference sheet, $C = λ ν$ $C=lambdanu$ where $C$ $C$ is the speed of the wave, $λ$ $lambda$ is the wavelength, and $ν$ $nu$ is the frequency. Solving this formula for wavelength, $λ = \frac{C}{ν}$ $lambda=C/nu$ .

For AM signals, $C = 3.0 \times 10^{8} m/s$ $C=3.0times10^8"m/s"$ and $ν$ $nu$ ranges from $550 \times 10^{3} Hz$ $550times10^3"Hz"$ to $1600 \times 10^{3} Hz$ $1600times10^3"Hz"$ (since $1 kHz = 10^{3} Hz$ $1"kHz"=10^3"Hz"$ ). Therefore, the wavelength ranges from $λ = \frac{3.0 \times 10^{8} m/s}{550 \times 10^{3} Hz} = 545 m$ $lambda=(3.0times10^8"m/s")/(550times10^3"Hz")=545"m"$ to $λ = \frac{3.0 \times 10^{8} m/s}{1600 \times 10^{3} Hz} = 188 m$ $lambda=(3.0times10^8"m/s")/(1600times10^3"Hz")=188"m"$ .

For FM signals, $C = 3.0 \times 10^{8} m/s$ $C=3.0times10^8"m/s"$ and $ν$ $nu$ ranges from $88 \times 10^{6} Hz$ $88times10^6"Hz"$ to $108 \times 10^{6} Hz$ $108times10^6"Hz"$ (since $1 MHz = 10^{6} Hz$ $1"MHz"=10^6"Hz"$ ). Therefore, the wavelength ranges from $λ = \frac{3.0 \times 10^{8} m/s}{88 \times 10^{6} Hz} = 3.4 m$ $lambda=(3.0times10^8"m/s")/(88times10^6"Hz")=3.4"m"$ to $λ = \frac{3.0 \times 10^{8} m/s}{108 \times 10^{6} Hz} = 2.8 m$ $lambda=(3.0times10^8"m/s")/(108times10^6"Hz")=2.8"m"$ .

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