The length of antenna for transmitting a signal of 30 kHz is:

The correct answer is Option (3) → \( l = 2.5\,\mathrm{km} \)

For efficient radiation the length of the antenna should be about one quarter of the wavelength, \( l = \lambda/4 \).

    \( f = 30\,\mathrm{kHz} = 3\times10^{4}\,\mathrm{Hz} \)
    \( c = 3\times10^{8}\,\mathrm{m\,s^{-1}} \)

    \( \displaystyle \lambda = \frac{c}{f} = \frac{3\times10^{8}}{3\times10^{4}} = 10^{4}\,\mathrm{m} \)

    \( \displaystyle l = \frac{\lambda}{4} = \frac{10^{4}\,\mathrm{m}}{4} = 2500\,\mathrm{m} = 2.5\,\mathrm{km} \)

Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.

NCERT (Pre-rationalised edition, 2022-23):
Size of the Antenna or Aerial – “For transmitting a signal, we need an antenna or an aerial. This antenna should have a size comparable to the wavelength of the signal (at least λ/4 in dimension) so that the antenna properly senses the time variation of the signal.”