Question

question 16 of 20 view policies current attempt in progress convert 4.19 km wavelength into frequency, expressing the result in mhz. etextbook and media save for later attempts: 0 of 3 used submit answer

Explanation:

Step1: Recall the wave - speed formula

The speed of light $c$ is related to frequency $f$ and wavelength $\lambda$ by the formula $c = f\lambda$, where $c=3\times 10^{8}\ m/s$. First, convert the wavelength from kilometers to meters. Given $\lambda = 4.19\ km=4.19\times 10^{3}\ m$.

Step2: Solve for frequency

From $c = f\lambda$, we can express $f=\frac{c}{\lambda}$. Substitute $c = 3\times 10^{8}\ m/s$ and $\lambda = 4.19\times 10^{3}\ m$ into the formula: $f=\frac{3\times 10^{8}}{4.19\times 10^{3}}\ Hz$.

Step3: Convert frequency to MHz

Since $1\ MHz = 10^{6}\ Hz$, then $f=\frac{3\times 10^{8}}{4.19\times 10^{3}\times10^{6}}\ MHz$. Calculate $\frac{3\times 10^{8}}{4.19\times 10^{9}}=\frac{3}{4.19\times10}\ MHz\approx0.0716\ MHz$.

Answer:

$0.0716$