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The relationship between time period and frequency is fundamental in wave mechanics. The time period (T) of a wave is the duration of one complete cycle of the wave, while frequency (f) refers to the number of cycles that occur in one second.

The correct expression T = 1 ÷ f indicates that the time period is the inverse of frequency. If you have a frequency of, say, 2 Hz, that means 2 cycles occur each second. Thus, the time period for one complete cycle is 1 second divided by 2, resulting in a time period of 0.5 seconds. This inverse relationship means that as frequency increases (more cycles per second), the time period decreases (the duration of one cycle becomes shorter), and vice versa.

The other options presented do not reflect this fundamental relationship correctly. For instance, stating that T = f ÷ 1 or T = f × 1 would imply that the time period is directly proportional to frequency, which is not accurate in the context of wave mechanics. Meanwhile, T = 1 + f suggests an additive relationship, which further misrepresents how time period and frequency relate to each other.