Q.A transmitter consists of an LC circuit with an inductance of 1 $\mu$H and a capacitance of 1 $\mu$F. What is the wavelength of the electromagnetic waves it emits?

Maxwell's theoretical prediction of electromagnetic waves was confirmed experimentally by Heinrich Rudolf Hertz in 1888. His apparatus used two small spherical metal electrodes connected to larger spheres, driven by an induction coil with a very large number of turns to build up a very high electromotive force between them; as the potential rises, the air between the electrodes ionises and a spark (an electrical discharge) jumps across, and this discharge is detected as a matching induced spark at a separate, distant, ring-shaped (not fully closed) receiver electrode -- direct evidence that energy is being transmitted through the intervening empty space as a wave. When Hertz rotated the receiver by 90$^\circ$, no spark was observed at all, confirming that the wave is transverse (its effect depends on the receiver's orientation relative to the field, which a purely longitudinal wave would not show); Hertz further measured the wave's speed and found it equal to the speed of light, $3\times10^8$ m/s, exactly matching Maxwell's calculated value $c=1/\sqrt{\mu_0\epsilon_0}$. Underlying every source of electromagnetic radiation is a single rule about how a charge must move: a stationary charge produces only a static electric field and radiates nothing; a charge moving with uniform (constant) velocity produces a steady current and hence a magnetic field, but that field does not vary with time (it only varies with position), so by Faraday's/Maxwell's equations it cannot regenerate any further field and still no wave is radiated; only an accelerating charge -- one whose velocity is changing in magnitude or direction -- produces genuinely time-varying electric and magnetic fields together, and these coupled, time-varying fields are what constitute a propagating electromagnetic wave. Because any oscillatory motion about a mean position is itself continuous accelerated motion, an oscillating charge -- the spark in Hertz's apparatus, an oscillating molecular dipole, electrons oscillating in a radio antenna, or an atom's electron oscillating between energy levels -- is always, in principle, a source of electromagnetic waves; the resulting wave's direction of propagation is perpendicular to the plane containing the oscillating $\vec E$ and $\vec B$ vectors, and the wave's frequency exactly equals the frequency of the oscillating source charge that produced it. A simple direct application: a transmitter built from an LC circuit generates an oscillating current at its own resonant frequency $f=1/(2\pi\sqrt{LC})$, and this oscillating current (accelerating charge) radiates an electromagnetic wave of exactly that frequency, with wavelength given by $\lambda=c/f$.