Understanding Sine Wave Frequency and Time Period

The question asks us to find the time period of a sine wave given its frequency. The frequency is provided as 1000 Hz.

Key Concepts

• Frequency (f): This represents the number of cycles or oscillations a wave completes in one second. It is measured in Hertz (Hz).
• Time Period (T): This is the time it takes for one complete cycle or oscillation of the wave. It is measured in seconds (s) or milliseconds (ms).

Relationship Between Frequency and Time Period

Frequency and time period are inversely related. This means that as the frequency increases, the time period decreases, and vice versa. The mathematical formula connecting them is:

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

Where:

• \( T \) is the time period in seconds (s).
• \( f \) is the frequency in Hertz (Hz).

Calculating the Time Period

We are given the frequency \( f = 1000 \) Hz. Let's use the formula to calculate the time period \( T \):

1. Substitute the frequency value into the formula:

   $$ T = \frac{1}{1000 \text{ Hz}} $$

2. Calculate the result in seconds:

   $$ T = 0.001 \text{ s} $$

3. Convert seconds to milliseconds (ms): Since 1 second is equal to 1000 milliseconds, we multiply the result in seconds by 1000:

   $$ T = 0.001 \text{ s} \times 1000 \frac{\text{ms}}{\text{s}} $$

   $$ T = 1 \text{ ms} $$

Conclusion

Therefore, the time period of a sine wave with a frequency of 1000 Hz is 1 ms. This matches one of the given options.