The tuning dial of a radio set covers stations from 6 MHz to 15 MHz. The wavelength band covered by the set is (Take \(c=3\times10^{8}\ \mathrm{m\,s^{-1}}\))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 50 m to 20 m
For an electromagnetic wave, frequency and wavelength are linked by \( \nu\lambda=c \). So \( \lambda=c/\nu \), and the lowest frequency gives the longest wavelength.
\( \nu_1=6\times10^{6}\ \mathrm{Hz} \)
\( \nu_2=1.5\times10^{7}\ \mathrm{Hz} \)
\( \begin{aligned} \lambda_1 &= \frac{c}{\nu_1} \\ &= \frac{3\times10^{8}}{6\times10^{6}} \\ &= 50\ \mathrm{m} \end{aligned} \)
\( \begin{aligned} \lambda_2 &= \frac{c}{\nu_2} \\ &= \frac{3\times10^{8}}{1.5\times10^{7}} \\ &= 20\ \mathrm{m} \end{aligned} \)
Therefore, the set covers the band from 50 m at the 6 MHz end to 20 m at the 15 MHz end.
NCERT (2026-27):
Nature of electromagnetic waves – “… This relation is often written in terms of frequency, ν (=ω/2π) and wavelength, λ (=2π/k) as”
\( \displaystyle 2\pi\nu=c\left(\frac{2\pi}{\lambda}\right) \quad \text{or} \) \( \nu\lambda=c \)\( \qquad [8.9(b)] \)