Question

Can two waves have the same frequency but different periods?

Answer 1

No, two waves cannot have the same frequency but different periods. Frequency and period are reciprocal quantities, meaning they are inversely proportional to each other.

The frequency of a wave refers to the number of complete cycles or oscillations it undergoes per unit of time. It is usually measured in hertz (Hz), which represents cycles per second. Mathematically, frequency ($f$) is defined as the reciprocal of the period ($T$):

$f=\frac{1}{T}$

The period of a wave, on the other hand, is the time it takes for one complete cycle or oscillation to occur. It is the reciprocal of the frequency and is measured in units of time (e.g., seconds, milliseconds).

Since frequency and period are reciprocals of each other, if two waves have the same frequency, their periods must be the same as well. If the frequency of two waves is identical, it means they complete the same number of cycles or oscillations in the same time interval.

Therefore, waves with the same frequency will always have the same period, and waves with different periods will have different frequencies.