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An audio signal of $15 \mathrm{kHz}$ frequency cannot be transmitted over long distances without modulation, because
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The correct answers are:
the size of the required antenna would be least $5 \mathrm{~km}$ which is not convenient
,
the audio signal can not be transmitted through sky waves
,
effective power transmitted would be very low, if the size of the antenna is less than $5 \mathrm{~km}$
the size of the required antenna would be least $5 \mathrm{~km}$ which is not convenient
,
the audio signal can not be transmitted through sky waves
,
effective power transmitted would be very low, if the size of the antenna is less than $5 \mathrm{~km}$
Transmission of a signal depends on three factors. These are size of antenna, power of transmission and power of transmitted wave.
As given that frequency of the audio signal to be transmitted is
$$
\mathrm{v}_{\mathrm{m}}=15 \mathrm{kHz}=15 \times 10^3 \mathrm{~Hz}
$$
Wavelength $\lambda_{\mathrm{m}}=\frac{\mathrm{c}}{\mathrm{v}_{\mathrm{m}}}=\frac{3 \times 10^8}{15 \times 10^3}=\frac{1}{5} \times 10^5 \mathrm{~m}$ $=0.2 \times 10^5 \mathrm{~m}$
Size of the antenna
$$
l=\frac{\lambda}{4}=\frac{0.2 \times 10^5}{4}=5 \times 10^3 \mathrm{~m}=5 \mathrm{~km}
$$
So, the audio frequency signals are of low frequency waves. So, the audiowave cannot be transmitted by sky waves as they are absorbed by atmosphere.
If the size of the antenna is less than $5 \mathrm{~km}$, the effective power transmission would be very low because of deviation from resonance wavelength of wave and antenna length.
As given that frequency of the audio signal to be transmitted is
$$
\mathrm{v}_{\mathrm{m}}=15 \mathrm{kHz}=15 \times 10^3 \mathrm{~Hz}
$$
Wavelength $\lambda_{\mathrm{m}}=\frac{\mathrm{c}}{\mathrm{v}_{\mathrm{m}}}=\frac{3 \times 10^8}{15 \times 10^3}=\frac{1}{5} \times 10^5 \mathrm{~m}$ $=0.2 \times 10^5 \mathrm{~m}$
Size of the antenna
$$
l=\frac{\lambda}{4}=\frac{0.2 \times 10^5}{4}=5 \times 10^3 \mathrm{~m}=5 \mathrm{~km}
$$
So, the audio frequency signals are of low frequency waves. So, the audiowave cannot be transmitted by sky waves as they are absorbed by atmosphere.
If the size of the antenna is less than $5 \mathrm{~km}$, the effective power transmission would be very low because of deviation from resonance wavelength of wave and antenna length.
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