When labelling the axis of an AM Signal's frequency spectrum diagram, how can I calculate the frequencies?

Question

If I have an AM signal with the following carrier and message tones;

Carrier: V_c = 120 cos(2π 0.5 x10⁶)t
Message: V_m = 40 cos(2π 4 x10³)t

With a system resistance of 50 Ω,

I can calculate the power of each component.

Carrier Power: A_c² / 2R
= 120²/2 x 50
= 144 Watts

Modulation Index (m) = V_m / V_c
= 40 / 120 = 0.333

Sideband Power = m² V_c² / 8R
= 0.333² x 120² / 8 x 50 = 152 Watts

So what If I want to create a frequency spectrum diagram? Amplitude on the y axis would be plotted against Frequency (kHz) on the x axis.

The carrier signal and the two sideband signals would be plotted as vertical lines - with the carrier signal being shown to have a larger amplitude than the other two signals.

The three lines would be annotated with their power levels. So what if I wanted to label my x axis (frequency)? How do I calculate the appropriate frequencies to plot?

Answer 1

Answering my own question thanks to help from @Farcher.

The frequencies were part of my initial signals/tones.

Carrier:
120 cos(2π 0.5 x10⁶)t
frequency is 0.5 x 10⁶
= 500,000 Hz
= 500 kHz - Which is plotted below the carrier signal on the x axis.

Message:
40 cos(2π 4 x10³)t
frequency is 4 x10³ = 4000 Hz
= 4 kHz,
Which is subtracted from 500Hz to give a value of 496kHz for the leftmost sideband signal on the x asis, and added to 500Hz to give a value of 504kHz for the rightmost sideband signal on the x axis.