Counting cycles of a sine wave: A sinusoidal signal has a frequency of 100 Hz. Over an interval of 12 s, how many complete cycles does it undergo?

Introduction / Context:
Frequency represents the number of cycles per second. Converting a time interval into total cycles is a direct multiplication and shows up in sampling, synchronization, and timing design. This question ensures correct interpretation of the hertz unit and appropriate scaling across seconds.

Given Data / Assumptions:

• Frequency f = 100 Hz = 100 cycles per second.
• Observation interval t = 12 s.
• We count complete cycles, assuming steady frequency.

Concept / Approach:
Total cycles N over time t is N = f * t when frequency is constant. This linear relation is fundamental to periodic phenomena and aligns with everyday concepts like RPM and sampling counts.

Step-by-Step Solution:

Verification / Alternative check:
Cross-check using period: T = 1/f = 1/100 s = 0.01 s. The number of periods in 12 s is 12 / 0.01 = 1200, matching the prior calculation exactly.

Why Other Options Are Wrong:

• 12 cycles or 120 cycles: These confuse seconds with cycles; they are too small by factors of 100 or 10.
• 1/100 cycle: This is one period’s fraction, not 12 seconds of activity.

Common Pitfalls:

• Treating hertz as radians per second or misplacing the decimal during multiplication.
• Failing to use consistent units (seconds for time, hertz for cycles per second).

Final Answer:
1,200 cycles