Understanding the Frequency of a Sine Wave: Cycles Per Second

When dealing with sine waves, understanding the frequency, expressed as the number of cycles per second, is crucial. This article will explore a specific example of a sine wave that completes one cycle in 5 microseconds (μs) and determine how many cycles it completes in 1 second.

Definition of a Microsecond

A microsecond is a very small unit of time, defined as 10^-6 of a second. Let's break down the calculation step-by-step to find out how many cycles a sine wave completes in 1 second when it takes 5 microseconds μs to complete one cycle.

Step-by-Step Calculation

First, we need to convert 1 second to microseconds. We know that:

1 second 1000000 μs

Next, we determine the number of cycles in 1 second:

Number of cycles 1000000 μs / 5 μs/cycle 200000 cycles

Therefore, the sine wave completes 200000 cycles in 1 second.

Understanding the Units and Calculation

To understand this calculation better, let's delve into the units involved. A microsecond is one millionth of a second (10^-6). If we have a sine wave that completes one cycle every 5 microseconds, we can think of it as:

1 / 5 μs per cycle, which is equivalent to:

1 / 5 x 10^-6 seconds per cycle.

This tells us the time for one cycle in seconds. To find out the number of cycles in 1 second, we take the reciprocal of this value:

Cycles per second 1 / (1 / 5 x 10^-6) 5 x 10^6 cycles/second

This simplifies to 200000 cycles in 1 second.

Mathematical Insight

To further simplify, we can use the fact that one second is 10^6 microseconds. Thus, 5 microseconds is 5 x 10^-6 seconds. The number of cycles can be calculated as:

Number of cycles 10^6 / 5 x 10^-6 10^6 / 5 x 10^-6 200000 cycles

So, there are 200000 5-microsecond cycles in 1 second.

Conclusion

Understanding the frequency of a sine wave is fundamental in various applications, ranging from signal processing to electrical engineering. The example provided shows that a sine wave with a cycle period of 5 microseconds will complete 200000 cycles in 1 second. This knowledge is invaluable for anyone working with time-sensitive signals and waveforms.