A radio station broadcasts at 80 MHz. How long does it take for this radio signal to travel a distance of
2.0
×
10
7
m through space? (c = 3.0 × 108 m/s)

Question

A radio station broadcasts at 80 MHz. How long does it take for this radio signal to travel a distance of 
2.0
×
10
7
 m through space? (c = 3.0 × 108 m/s)

BlackTom AI · Accepted Answer

Consider the basic relation for signal travel time: time = distance / speed.

First, identify the given values: distance = 2.0 × 10^7 meters and speed = c = 3.0 × 10^8 meters per second.

Compute the time: (2.0 × 10^7 m) ÷ (3.0 × 10^8 m/s) = (2.0/3.0) × 10^(7−8) s = 0.666... × 10^−1 s = 6.7 × 10^−2 s.

Now evaluate the answer options:
- Option 1: 6.7 × 10^−2 s. This matches the computed result exactly, so it is the correct time.
- Option 2: 0.15 × 10^−2 s equals 1.5 × 10^−3 s (0.0015 s). This is far smaller than the correct value because the distance is large and light travels about 3.0 × 10^8 m in one second, not a millisecond.
- Option 3: 15 ms equals 0.015 s. This would correspond to a distance of about 0.015 s × 3.0 × 10^8 m/s ≈ 4.5 × 10^6 m, which is only a fraction of the given 2.0 × 10^7 m, hence incorrect.
- Option 4: 20 ms equals 0.020 s. Similar to the previous, this implies a much shorter distance than provided, so it does not align with 2.0 × 10^7 m.
- Option 5: 25 ms equals 0.025 s. Again, this is inconsistent with the large distance when traveling at light speed.

In summary, only the first option yields the correct order of magnitude and exact value for the travel time of a radio signal spanning 2.0 × 10^7 meters at the speed of light, while the others underestimate the time by factors corresponding to the shorter assumed distances.

A radio station broadcasts at 80 MHz. How long does it take for this radio signal to travel a distance of 2.0 × 10 7 m through space? (c = 3.0 × 108 m/s)单项选择题

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