Question

a. Explain why the Fourier analysis of a square wave shows that modulation is needed to send data (or why we cannot send square pulses with regular wires).

b. Why do we use sine waves?

Do not copy from internet and need it typed, not hand written please.

Answer 1

(A) A fourier square wave is a non-sinusoidal periodic waveform in which the amplitude alternates at a steady frequency between fixed minimum and maximum values, with the same duration at minimum and maximum. Although not realizable in physical systems, the transition between minimum and maximum is instantaneous for an ideal square wave. that is why  why the Fourier analysis of a square wave shows that modulation is needed to send data

(B) The reasons are mostly practical and economical limitations, rather than the laws of physics.
Square waves would work just as fine since the solution of the wave equation allows any waveform. This is known as Helmholtz equation.
The problem associated with that is allocation of radio spectrum by government and industry is limited to narrow bands around single frequencies... Non-sinusoidal waves with base frequency ( f ) have multiple harmonics which are additional sine-waves at 2f, 3f, 4f_ _ _which are outside the allocated band,... We do use square waves when we the medium is exclusive, such as our own cables. For example, the USB cable uses near-square waves that are more easily (and less costly) associated with the binary(1 and 0).....In radio waves, even if government rules allowed to use square waves there would still be issues since each frequency propagates differently near objects and the ground... Also the antenna designs are frequency dependent.

It is probably not a coincidence that the mathematically simplest waveform, the sine-wave, is also the most economical to use.