The figure shows the effect of modulating a 1kHz sine wave with a 50Hz sine wave. You can adjust the Modulation Index to see how this changes the time and frequency domain outputs.

In mathematical terms the modulation is defined by:

f(t) = (1 + m cosw_it) cosw_ct,
where m is the modulation index,
w_i = 2p50 rad/s and w_c = 2p1000 rad/s

Using the trigonometric identity
2cosAcosB = cos(A-B) + cos(A+B) gives:

f(t) = cosw_ct + m cosw_it cosw_ct
     = cosw_c +m/2(cos(w_c-w_i)t + cos(w_c+w_i)t)
Hence we see frequencies of 1kHz (the carrier), 950Hz (lower side band - lsb) and 1050Hz (upper side band - usb) in the figure.