Negative frequency in music

1. What is a negative sound frequency?
2. What do negative frequencies represent?
3. Is negative frequency real?
4. Can we hear negative frequency?

What is a negative sound frequency?

Negative frequency is an idea associated with complex exponentials. A single sine wave can be broken down into two complex exponentials ('spinning numbers'), one with a positive exponent and one with a negative exponent. That one with the negative exponent is where you get the concept of a negative frequency.

What do negative frequencies represent?

Remembering that physically, sinusoids are waves, the sign of the frequency represents the direction of wave propagation. Simply put, negative frequencies represent forward traveling waves, while positive frequencies represent backward traveling waves.

Is negative frequency real?

The meaning of negative frequencies is just mathematical(not physical) similarly to the imaginary part of a complex signal. In real world, the negative frequency does not exists and the spectral content on negative frequencies must be added to the spectral content at the positive frequencies, to save energy.

Can we hear negative frequency?

No. The frequency of a sound is the number of cycles per second. This can be so low as to beyond human hearing.