For transmitting a signal of frequency $1000 \text{ kHz}$, the minimum length of the antenna is (in $\text{ m}$)

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

The modulation index used in amplitude modulation of a message signal of peak voltage $10 \,V$ is $0.5$. By how much should the peak voltage of the carrier signal be changed, so as to obtain the modulation index of $0.8$, keeping the peak voltage of the message signal the same as before?

In general,a transmitting antenna is........

The frequency of a carrier wave is $1 MHz$. It is modulated by a wave of frequency $10 kHz$. If their amplitudes are $10 V$ and $0.5 V$ respectively,what are the modulation index and the frequencies of the $USB$ and $LSB$?

For an amplitude-modulated wave, the audio frequency is $500 \, \text{cycles/second}$. What is the actual carrier frequency in $\text{cycles/sec}$?