If the frequency doubles, what happens to the period?

If the frequency doubles, what happens to the period?

• A. Period doubles
• B. Period halves
• C. Period stays the same
• D. Period quadruples

Answer: (B)

Period and frequency are inverses: the period is the time for one cycle, while the frequency is how many cycles occur each second. They relate through T = 1/f. So, if the frequency doubles (f -> 2f), the period becomes T = 1/(2f) = T/2. In other words, each cycle takes half as long, so the period halves. If the frequency changes in other ways, the period changes accordingly (doubling frequency would not double the period, and keeping the period the same would require the frequency to stay the same).

Period and frequency are inverses: the period is the time for one cycle, while the frequency is how many cycles occur each second. They relate through T = 1/f. So, if the frequency doubles (f -> 2f), the period becomes T = 1/(2f) = T/2. In other words, each cycle takes half as long, so the period halves. If the frequency changes in other ways, the period changes accordingly (doubling frequency would not double the period, and keeping the period the same would require the frequency to stay the same).