$($a$)$

$($b$)$

frequency $\backslash ((\backslash$mathrm$\{$Hz$\})\backslash )$

Figure $1$ A pulse wave and its spectrum

a$.$ Calculate the fundamental frequency of the waveform in Figure $1($a$),$ Figure $1($b$),$ and Figure $1($c$).$

$(1$ mark$)$

Considering the correspondence between the period in the time domain and the number of spectral lines in each lobe in the frequency domain that can be seen across parts $($a$)-($c$)$ of Figure $1,$

b$.$ How would you expect the waveform to look like if the spectrum becomes continuous, coinciding with the dashed curve?

$(1$ mark$)$

c$.$ If the spectral lines in Figure $1($a$)$ are further spread, so the zeroth spectral line stays at $0,$ while the others move to frequencies $\backslash (1\backslash$mathrm$\{$~Hz$\},2\backslash$mathrm$\{$~Hz$\},3\backslash$mathrm$\{$~Hz$\}\backslash ),$ etc, how would you expect the waveform to look like?

$(1$ mark$)$

d$.$ Sketch the spectrum you would expect if the period of the waveform were equal to $4$ s $.$