A person tries to broadcast with the same ant | vedclass

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$(C)$ The power $P$ of a signal radiated by an antenna is proportional to the square of the frequency $v$, i.e., $P \propto v^2$.Given frequencies are

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$100$ times

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$(C)$ The power $P$ of a signal radiated by an antenna is proportional to the square of the frequency $v$, i.e., $P \propto v^2$.Given frequencies are $v_1 = 10^7 \,Hz$ and $v_2 = 10^6 \,Hz$.The ratio of powers is $\frac{P_1}{P_2} = \left(\frac{v_1}{v_2}\right)^2$.Substituting the values, we get $\frac{P_1}{P_2} = \left(\frac{10^7}{10^6}\right)^2 = (10)^2 = 100$.This implies $P_1 = 100 P_2$.Since the power radiated at $10^7 \,Hz$ is $100$ times the power radiated at $10^6 \,Hz$ for the same input signal strength, the broadcaster must increase the signal strength at $10^6 \,Hz$ by $100$ times to achieve equal strength at the receiver.

$A$ person tries to broadcast with the same antenna both the signals at $10^7 \,Hz$ and $10^6 \,Hz$. If the receiver at some distance has to receive an equal strength for both the frequencies, then the broadcaster has to approximately increase the signal strength at $10^6 \,Hz$ to $10^7 \,Hz$ by

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