A radio station broadcasts at 80 MHz.How long does it take for this radio signal to travel a distance of $2.0 \times 10 ^ { 7 } \mathrm {~m}$ through space? (c = 3.0 × 10⁸ m/s) A)0.15 × 10^-2 s B)15 ms C)6.7 × 10^-2 s D)20 ms E)25 ms

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Quizplus · Accepted Answer

We can use the formula $$v = f \lambda$$ where - $v$ is the speed of the wave (which is equal to the speed of light $c$ in this case) - $f$ is the frequency of the wave (in Hz) - $\lambda$ is the wavelength of the wave (in meters) To solve for $\lambda$, we rearrange the formula as $$\lambda = \frac{v}{f}$$ Substituting the given values, we get $$\lambda = \frac{3.0 imes10^8 \mathrm{~m/s}}{80 imes10^6\mathrm{~Hz}} = 3.75\mathrm{~m}$$ To find the time it takes for the signal to travel a distance of $2.0 imes10^7\mathrm{~m}$, we can use the formula $$t = \frac{d}{v}$$ Substituting the given values, we get $$t = \frac{2.0 imes10^7\mathrm{~m}}{3.0 imes10^8\mathrm{~m/s}} = 0.067\mathrm{~s} = 6.7 imes10^{-2}\mathrm{~s}$$ Therefore, the answer is (C) 6.7 × 10^-2 s.

A Radio Station Broadcasts at 80 MHz 2.0×107 m2.0 \times 10 ^ { 7 } \mathrm {~m}2.0×107 m

A Radio Station Broadcasts at 80 MHz $2.0 \times 10 ^ { 7 } \mathrm {~m}$