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Clock Signals — The frequency of a periodic clock waveform equals the reciprocal of its period. Evaluate the statement.

Difficulty: Easy

Correct Answer: Correct

Explanation:


Introduction:
Digital systems rely on clock waveforms to sequence operations. Two fundamental descriptors of a periodic signal are period (T) and frequency (f). This question tests the canonical relationship between them used across timing analysis and specification sheets.

Given Data / Assumptions:

  • Signal is periodic and stable.
  • Period T is measured in seconds per cycle.
  • Frequency f is cycles per second (hertz).


Concept / Approach:
By definition, frequency is the number of cycles per unit time. If each cycle takes T seconds, then in one second the count of cycles is 1/T. Therefore, f = 1 / T, independent of the exact waveshape (square, sine, triangle) as long as periodicity holds.

Step-by-Step Solution:

1) Let T be the duration of one full cycle.2) The number of cycles in one second is 1 divided by the cycle time: f = 1/T.3) Units check: seconds cancel, leaving hertz (s^-1).


Verification / Alternative check:

Example: If T = 10 ns, then f = 1 / (10 * 10^-9) = 100 MHz, which aligns with practice.


Why Other Options Are Wrong:

Incorrect: Contradicts the definitional relation f = 1/T.True only for analog clocks: Applies equally to digital clocks.True only for square waves: Shape is irrelevant; periodicity is the key.


Common Pitfalls:

Mixing up angular frequency w (w = 2 * pi * f) with linear frequency f.Using milliseconds or nanoseconds without converting to seconds first.


Final Answer:

Correct
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