megahertz to radians per second conversion

How to convert megahertz to radians per second?

Sure! To convert from megahertz (MHz) to radians per second (rad/s), you need to understand the relationship between these units of measure.

1 Hz (Hertz) is a unit of frequency that represents one cycle per second. 1 MHz (Megahertz) = $10^6$ Hz = 1,000,000 Hz.

Angular frequency in radians per second can be found by the formula: $\omega = 2\pi f$ where:

• $\omega$ is the angular frequency in radians per second.
• $f$ is the frequency in Hertz.

To convert 1 MHz to radians per second:

1. Convert MHz to Hz: $1 \text{ MHz} = 1,000,000 \text{ Hz}$

2. Use the formula to find the angular frequency: $\omega = 2\pi \times 1,000,000 \text{ Hz}$

$\omega = 2\pi \times 1,000,000$

$\omega \approx 6,283,185.307 \text{ rad/s}$

So, 1 MHz is approximately $6,283,185.307 \text{ rad/s}$.

Real-world Examples for Other Quantities of Megahertz

1. FM Radio:

   • Typical FM radio stations broadcast between 88 MHz and 108 MHz.
   • For example, 100 MHz can be converted to radians per second: $\omega = 2\pi \times 100,000,000$ $\omega \approx 628,318,530.7 \text{ rad/s}$

2. WiFi Frequencies:

   • WiFi operates in the 2.4 GHz (2400 MHz) and 5 GHz (5000 MHz) bands.

   • For 2.4 GHz: $\omega = 2\pi \times 2,400,000,000$ $\omega \approx 15,079,644,737 \text{ rad/s}$

   • For 5 GHz: $\omega = 2\pi \times 5,000,000,000$ $\omega \approx 31,415,926,536 \text{ rad/s}$

3. Bluetooth:

   • Bluetooth operates around 2.4 GHz (2400 MHz).
   • Using the same conversion as Wi-Fi: $\omega \approx 15,079,644,737 \text{ rad/s}$

4. Processor Clock Speed:

   • CPU clock speeds are often in the range of GHz (Gigahertz), such as 3.5 GHz.
   • For 3.5 GHz: $\omega = 2\pi \times 3,500,000,000$ $\omega \approx 21,991,148,576 \text{ rad/s}$

These conversions can help understand the magnitude of angular frequency associated with different frequencies commonly encountered in various technologies.