A carrier wave $V_c(t)=160 \sin \left(2 \pi \times 10^6 t\right)$ volts is made to vary between $V_{\max }=200 \mathrm{~V}$ and $V_{\min }=120 \mathrm{~V}$ by a message signal $\mathrm{V}_{\mathrm{m}}(\mathrm{t})=\mathrm{A}_{\mathrm{m}} \sin \left(2 \pi \times 10^3 \mathrm{t}\right)$ volts. The peak voltage $\mathrm{A}_{\mathrm{m}}$ of the modulation signal is ____.