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