The amplitude of upper and lower side bands of $AM$ wave where a carrier signal with frequency $11.21 \mathrm{MHz},$ peak voltage $15 \mathrm{V}$ is amplitude modulated by a $7.7 \mathrm{kHz}$ sine wave of $5 \mathrm{V}$ amplitude are $\frac{a}{10} \mathrm{V}$ and $\frac{b}{10} \mathrm{V}$ respectively. Then the value of $\frac{a}{b}$ is_____.

In radio communications, a sideband is a band of frequencies higher than or lower than the carrier frequency, that are the result of the modulation process. The signal components above the carrier frequency constitute the upper sideband (USB), and those below the carrier frequency constitute the lower sideband (LSB).

$\frac{a}{10}=\frac{b}{10}=\frac{\mu A_C}{2}$
$\Rightarrow \frac{a}{b}=1$