Question

Assume that a radio station is about $200$ km away from your location and the station operates at $972$ kHz. How long does it take for an electromagnetic signal to travel from the station to you and how many wave crests does it send out per second

• A. $666$ $\mu$s and $9.72 \times 10^5$ crests per second
• B. $666$ $\mu$s and $972 \times 10^5$ crests per second
• C. $555$ $\mu$s and $97.2 \times 10^7$ crests per second
• D. $555$ $\mu$s and $0.972 \times 10^5$ crests per second
• E. $444$ $\mu$s and $9 \times 10^6$ crests per second

Hint:

Frequency directly gives number of crests per second.

Answer 1

The Correct Option is A

Concept:
Speed of EM wave: \[ c = 3 \times 10^8 \text{ m/s} \]

Step 1: Time calculation.
\[ d = 200 \text{ km} = 2 \times 10^5 \text{ m} \] \[ t = \frac{d}{c} = \frac{2 \times 10^5}{3 \times 10^8} = \frac{2}{3} \times 10^{-3} = 666 \ \mu s \]

Step 2: Frequency.
\[ f = 972 \text{ kHz} = 9.72 \times 10^5 \text{ Hz} \]