Select the correct answer. If the frequency of a FM wave is [tex]$8.85 \times 10^7$[/tex] hertz, what is the period of the FM wave?
A. [tex]$2.58 \times 10^{-8}$[/tex] seconds
B. [tex]$1.13 \times 10^{-8}$[/tex] seconds
C. [tex]$1.25 \times 10^{-7}$[/tex] seconds
D. [tex]$5.82 \times 10^{-7}$[/tex] seconds
Answer (2)
The period (T) of a wave is the inverse of its frequency (f): T = f 1 .
Substitute the given frequency f = 8.85 × 1 0 7 hertz into the formula.
Calculate the period: T = 8.85 × 1 0 7 1 ≈ 1.13 × 1 0 − 8 seconds.
The correct answer is B. 1.13 × 1 0 − 8 seconds. 1.13 × 1 0 − 8 seconds
Explanation
Understanding the Problem We are given the frequency of an FM wave, which is 8.85 \t × 1 0 7 hertz, and we need to find the period of the wave. The period is the inverse of the frequency.
Stating the Formula The formula relating the period (T) and the frequency (f) of a wave is:
T = f 1
where T is the period in seconds and f is the frequency in hertz.
Calculating the Period We are given that the frequency f = 8.85 \t × 1 0 7 hertz. We can substitute this value into the formula to find the period:
T = 8.85 \t × 1 0 7 1
Calculating this value, we get:
T ≈ 1.13 × 1 0 − 8 seconds
Selecting the Correct Answer Now we compare our calculated period to the given options:
A. 2.58 × 1 0 − 8 seconds B. 1.13 × 1 0 − 8 seconds C. 1.25 × 1 0 − 7 seconds D. 5.82 × 1 0 − 7 seconds
The closest value to our calculated period is 1.13 × 1 0 − 8 seconds, which corresponds to option B.
Examples
Understanding the relationship between frequency and period is crucial in many real-world applications. For example, in telecommunications, the frequency of a radio wave determines its channel, while the period affects how quickly data can be transmitted. Similarly, in music, the frequency of a sound wave determines its pitch, and the period affects the perceived duration of a note. By understanding these concepts, engineers and musicians can design and optimize systems for transmitting and processing information.
The period of the FM wave calculated using the formula T = f 1 is approximately 1.13 × 1 0 − 8 seconds. Therefore, the correct answer is option B. This is derived from a frequency of 8.85 × 1 0 7 hertz.
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