If an alternating current sine wave repeats itself 500 times in 1/5 of a second, what is its frequency in hertz (Hz)?

To determine the frequency of an alternating current sine wave in hertz (Hz), the number of cycles completed in one second must be calculated. Frequency is defined as the number of cycles per second, measured in hertz.

In this case, the sine wave repeats itself 500 times in 1/5 of a second. To find the frequency in hertz, we first need to convert the time period into seconds. Since 1/5 of a second is equivalent to 0.2 seconds, we can calculate the frequency as follows:

Frequency (Hz) = Number of Cycles / Time (in seconds)

Substituting the values:

Frequency (Hz) = 500 cycles / 0.2 seconds = 2500 Hz

This indicates that the sine wave completes 2500 cycles in one full second, which directly provides the frequency as 2500 hertz. Therefore, the correct answer reflects this straightforward calculation and conceptual understanding of frequency in relation to time and cycles.