An EM wave of audio signal of 15 kHz frequency cannot be transmitted over long distances without modulation. Which of the following can’t be the reason

Frequency of audio signal ${\mathrm{v}}_{\mathrm{m}}=15\mathrm{kHz}=15\times {10}^3\mathrm{Hz}$
${\mathrm{\lambda }}_{\mathrm{m}}=0.2\times {10}^5\mathrm{m}$
Size of antenna  ${\mathrm{h}}_{=\mathrm{\lambda }/4=20000/4}=5000\mathrm{m}$
Size of antenna = 5 km
Audio frequency signal are of low frequency waves. So the audio wave cannot be transmitted by sky wave as they are absorbed by atmosphere. If the size of the antenna is less than 5 km, the effective power transmission would be very low because of the deviation from resonance of wavelength of wave and antenna length.