period of a 100 MHz FM radio were is roughly 1 X 10 to the negative 8th s. formulate a problem and solution.

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Problem: Calculate the number of cycles and the total distance traveled by an electromagnetic wave in one period of a 100 MHz FM radio signal.

Solution:
1. Determine the frequency in cycles per second:
Frequency = 100 MHz = 100,000,000 Hz

2. Calculate the period of the signal:
Period = 1 / Frequency = 1 / 100,000,000 Hz = 1 × 10^(-8) seconds

3. Calculate the number of cycles in one period:
Number of cycles = Frequency × Period = 100,000,000 Hz × 1 × 10^(-8) seconds = 1 cycle

4. Calculate the total distance traveled by the wave in one period:
Speed of light = 3 × 10^8 meters per second (approximately)

Distance = Speed × Time
Distance = Speed × Period = (3 × 10^8 meters per second) × (1 × 10^(-8) seconds) = 3 meters

Therefore, in one period of a 100 MHz FM radio signal, there is 1 cycle and the total distance traveled by the electromagnetic wave is approximately 3 meters.

Problem:

Find the number of complete cycles of a 100 MHz FM radio wave that occur in one second.

Solution:
To solve this problem, we need to determine the number of complete cycles of the FM radio wave that occur in one second. The given information tells us that the period of the wave is approximately 1 x 10^-8 s.

To find the number of complete cycles, we can use the formula:

Number of Cycles = 1 second / Period

Substituting the given period, we have:

Number of Cycles = 1 second / (1 x 10^-8 s)

To simplify this calculation, we need to convert 1 s into scientific notation. One second can be written as 1.0 x 10^0 s.

Number of Cycles = (1.0 x 10^0 s) / (1 x 10^-8 s)

Now we need to divide the numerator by the denominator:

Number of Cycles = (1.0 x 10^0 s) / (1 x 10^-8 s)
= (1.0 x 10^0 s) * (1 x 10^8 s^-1)
= 1.0 x 10^8

Therefore, there are approximately 1 x 10^8 complete cycles of the 100 MHz FM radio wave that occur in one second.