A carrier wave \( V_c(t) = 160 \sin(2\pi \times 10^{6} t) \) volts is made to vary between \( V_{\text{max}} = 200 \, \text{V} \) and \( V_{\text{min}} = 120 \, \text{V} \) by a message signal \( V_{min}(t) = A_m \sin(2\pi \times 10^{3} t) \) volts. The peak voltage \( A_m \) of the modulating signal is ________.
