If the time period of a wave increases, its frequency will

Options

A. increase
B. decrease
C. remain the same
D. first increases then decreases

Answer

To solve the question "If the time period of a wave increases, its frequency will...", we can follow these steps:

### Step 1: Understand the relationship between time period and frequency
The time period (T) of a wave is the duration of one complete cycle of the wave. Frequency (f) is the number of cycles that occur in one second. The relationship between time period and frequency is given by the formula:
\[ f = \frac{1}{T} \]
This means that frequency is the reciprocal of the time period.

### Step 2: Analyze the effect of increasing the time period
If the time period (T) increases, we can express this mathematically. Let's say the time period changes from T1 to T2, where T2 > T1. According to the formula, if T increases, then:
\[ f = \frac{1}{T} \]
As T increases, the value of \( \frac{1}{T} \) decreases.

### Step 3: Conclude the effect on frequency
Since frequency (f) is inversely proportional to the time period (T), an increase in the time period leads to a decrease in frequency. Therefore, if the time period of a wave increases, its frequency will decrease.

### Final Answer:
If the time period of a wave increases, its frequency will **decrease**.

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