What is the effect of lower frequencies on the duration of a sound wave's period?

• A. Period decreases
• B. Period increases
• C. Period remains constant
• D. Period fluctuates

Answer: (B)

The correct answer is that the period of a sound wave increases with lower frequencies. To understand why this is the case, it is essential to consider the relationship between frequency and period.

Frequency refers to how many cycles of a wave occur in one second, typically measured in hertz (Hz). The period, on the other hand, is the amount of time it takes for one complete cycle of the wave to occur, measured in seconds. The relationship between frequency (f) and period (T) is given by the formula:

[ T = \frac{1}{f} ]

From this equation, it can be observed that as the frequency decreases, the value of T (the period) must increase. For example, a wave with a frequency of 1 Hz has a period of 1 second, whereas a wave with a frequency of 0.5 Hz has a period of 2 seconds. Therefore, as the frequency becomes lower, meaning fewer cycles per second, the duration of each cycle (period) naturally lengthens.

This fundamental relationship explains why the correct answer is that the period increases with lower frequencies.