The time-period of a wave refers to the time it takes for one complete cycle of the wave to occur. It is often represented by the symbol T and is measured in seconds. The frequency of a wave, on the other hand, refers to the number of complete cycles of the wave that occur in one second and is represented by the symbol f.

In the context of wave motion, the time-period and frequency are related to each other. The relationship between these two is given by the equation:

frequency = 1/time-period

This means that the frequency of a wave is inversely proportional to its time-period. In other words, as the time-period of a wave increases, its frequency decreases, and vice versa.

Explanation:

- Time-Period: The time-period of a wave is the time it takes for one complete cycle of the wave to occur. It is a measure of how long it takes for the wave to repeat itself. For example, if you have a wave that completes one cycle in 2 seconds, then the time-period of that wave is 2 seconds.

- Frequency: The frequency of a wave is the number of complete cycles of the wave that occur in one second. It is a measure of how often the wave repeats itself. For example, if you have a wave that completes 5 cycles in one second, then the frequency of that wave is 5 Hz (Hertz).

- Inverse Proportion: In mathematics, two quantities are said to be inversely proportional if an increase in one quantity leads to a decrease in the other quantity, and vice versa. In the case of time-period and frequency, they are inversely proportional. This means that as the time-period of a wave increases, its frequency decreases, and as the time-period decreases, its frequency increases.

- Proportional to Wave-Length: The wavelength of a wave is the distance between two consecutive points in a wave that are in phase with each other. It is often represented by the symbol λ and is measured in meters. The wavelength of a wave is proportional to its time-period and frequency. This means that as the time-period or frequency of a wave increases, its wavelength also increases, and vice versa.

Conclusion:

In conclusion, the time-period of a wave is inversely proportional to its frequency. As the time-period of a wave increases, its frequency decreases, and as the time-period decreases, its frequency increases. The frequency and time-period of a wave are related to each other by the equation frequency = 1/time-period.

Answer:-(B) Inversely proportional to frequency