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(A) The modulation index $m$ is defined as the ratio of the peak voltage of the modulating signal $(E_m)$ to the peak voltage of the carrier signal $(

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$-2$

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(A) The modulation index $m$ is defined as the ratio of the peak voltage of the modulating signal $(E_m)$ to the peak voltage of the carrier signal $(E_c)$: $m = \frac{E_m}{E_c}$.When the modulating signal is increased by $1 \%$,the new peak voltage is $E_m' = E_m(1 + 0.01) = 1.01 E_m$.When the carrier signal is increased by $3 \%$,the new peak voltage is $E_c' = E_c(1 + 0.03) = 1.03 E_c$.The new modulation index $m'$ is given by $m' = \frac{E_m'}{E_c'} = \frac{1.01 E_m}{1.03 E_c} \approx 0.9806 m$.The percentage change in the modulation index is $\frac{m' - m}{m} 	imes 100 = (0.9806 - 1) 	imes 100 \approx -1.94 \% \approx -2 \%$.Thus,the modulation index changes by approximately $-2 \%$.

$A$ carrier wave is used to transmit a message signal. If the peak voltage of the modulating signal and the carrier signal are increased by $1 \%$ and $3 \%$ respectively,the modulation index is changed by (in $\%$)

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