Q.How is length of antenna related to frequency of the signal?

Modulation is the process of superimposing the information contained in a low-frequency modulating signal (also called the intelligence or baseband signal) onto a high-frequency carrier signal. Formally, some characteristic of the carrier is varied in step with the instantaneous value of the modulating signal, and the output is the modulated signal.

A sinusoidal carrier can be written as $V = V_C \sin(\omega_c t + \theta)$, which has three parameters — amplitude $V_C$, frequency $f_c$ and phase $\theta$. Depending on which one is varied in proportion to the message, the process is named amplitude modulation (AM), frequency modulation (FM) or phase modulation (PM).

Modulation is unavoidable in any real communication link for several reasons:

• Antenna length — efficient radiation needs an antenna about $\lambda/4$ long. A low audio frequency has an enormous wavelength (a 20 kHz signal needs roughly a 3750 m antenna), whereas riding it on a high-frequency carrier shrinks the antenna to a practical size. …