Which expression gives the frequency in terms of the period T?

Which expression gives the frequency in terms of the period T?

• A. f = T
• B. f = 1/√T
• C. f = 1/T^2
• D. f = 1/T

Answer: (D)

Frequency is how many cycles occur each second, while period is how long one cycle lasts. They are reciprocal, so f = 1/T. This makes sense in units: if T is in seconds, f comes out in per-second units, i.e., hertz. For example, a cycle that takes 2 seconds happens every 2 seconds, so f = 0.5 Hz; a cycle lasting 0.25 seconds has f = 4 Hz. The other options don’t fit because they don’t reflect the inverse relationship and would give incorrect units or dependence on T (like proportional to T or involving a square root).

Frequency is how many cycles occur each second, while period is how long one cycle lasts. They are reciprocal, so f = 1/T. This makes sense in units: if T is in seconds, f comes out in per-second units, i.e., hertz. For example, a cycle that takes 2 seconds happens every 2 seconds, so f = 0.5 Hz; a cycle lasting 0.25 seconds has f = 4 Hz. The other options don’t fit because they don’t reflect the inverse relationship and would give incorrect units or dependence on T (like proportional to T or involving a square root).