Which formula expresses frequency in terms of the time period T?

Which formula expresses frequency in terms of the time period T?

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

Answer: (B)

The main relation tested is how frequency and time per cycle (the period) are connected. Frequency is how many cycles occur each second, while the period T is the duration of a single cycle. They are inverses, so the frequency is the reciprocal of the period: f = 1/T. This also means f multiplied by T equals 1, and the units line up correctly: seconds in the denominator give cycles per second (Hertz). If the period grows longer, the frequency decreases, and if the period shrinks, the frequency increases. The other forms don’t fit because they don’t reflect that longer periods mean fewer cycles per unit time, and they would imply inconsistent units or physically meaningless relationships (for example, f = T would suggest more cycles per second as the cycle takes longer, which is opposite to reality).

The main relation tested is how frequency and time per cycle (the period) are connected. Frequency is how many cycles occur each second, while the period T is the duration of a single cycle. They are inverses, so the frequency is the reciprocal of the period: f = 1/T. This also means f multiplied by T equals 1, and the units line up correctly: seconds in the denominator give cycles per second (Hertz). If the period grows longer, the frequency decreases, and if the period shrinks, the frequency increases. The other forms don’t fit because they don’t reflect that longer periods mean fewer cycles per unit time, and they would imply inconsistent units or physically meaningless relationships (for example, f = T would suggest more cycles per second as the cycle takes longer, which is opposite to reality).