91Ó°ÊÓ

The wavelength of the microwave is $\mathrm{λ}=3cm=0.03m$

Speed of microwave signal is $c=3×{10}^{8}m/s$

The distance between two mountaintops isrole="math" localid="1650003038058" $d=50km=50×{10}^{3}m$

The frequency is defined as the number of complete waves passing in unit time.

The formula to calculate the frequency in a periodic wave is given by

$f=\frac{c}{\mathrm{λ}}$

Substitute 0.03 m for $\mathrm{λ}$and $3×{10}^{8}m/s$for c into the above formula to calculate the frequency.

$$\begin{gathered} f=\frac{3×{10}^{8}m/s}{0.03m} \\ ={10}^{10}Hz \end{gathered}$$

The speed is defined as the rate of change of distance with respect to time.

The formula to calculate the time taken by the signal to travel from one mountaintop to another mountaintop is given by

$t=\frac{d}{c}$

Substitute $50×{10}^{3}m$for d and $3×{10}^{8}m/s$for c into the above formula to calculate the time.

$$\begin{gathered} t=\frac{50×{10}^{3}m}{3×{10}^{8}m/s} \\ =1.67×{10}^{-4}s \end{gathered}$$