hertz to degrees per second conversion

How to convert hertz to degrees per second?

Sure, I'd be happy to explain!

Converting Hertz to Degrees per Second

1 Hertz (Hz) is defined as one cycle per second. To convert Hz to degrees per second, consider that one complete cycle of a waveform (e.g., sine wave) is 360 degrees.

So, if we have 1 Hz:

• 1 Hz means there is one cycle per second.
• Since one cycle is 360 degrees, 1 Hz is equivalent to 360 degrees per second.

Formula: $\text{Degrees per Second} = \text{Frequency in Hz} \times 360$

For 1 Hz: $1 \text{ Hz} = 1 \times 360 = 360 \text{ degrees per second}$

Real-world Examples of Frequencies:

1. Human Hearing Range:

   • The human ear can typically hear sounds ranging from 20 Hz to 20,000 Hz (20 kHz). The lower end, 20 Hz, corresponds to 7,200 degrees per second (20 $\times$ 360 = 7,200 degrees per second), and the upper end, 20 kHz, corresponds to 7,200,000 degrees per second (20,000 $\times$ 360 = 7,200,000 degrees per second).

2. Power Line Frequency:

   • In many countries, the AC electrical power grid operates at 50 Hz or 60 Hz. For 50 Hz, this corresponds to 18,000 degrees per second (50 $\times$ 360 = 18,000 degrees per second) and for 60 Hz, it is 21,600 degrees per second (60 $\times$ 360 = 21,600 degrees per second).

3. Musical Notes:

   • The standard pitch (A4) in music is 440 Hz, which translates to 158,400 degrees per second (440 $\times$ 360 = 158,400 degrees per second).

4. Radio Frequencies:

   • AM (Amplitude Modulation) radio frequencies range from around 530 kHz to 1700 kHz. For example, a 1 MHz (1,000,000 Hz) signal corresponds to 360,000,000 degrees per second (1,000,000 $\times$ 360 = 360,000,000 degrees per second).

Understanding these conversions can be quite useful in various fields, from engineering and physics to music and communications!