I want to generate (and eventually sample) a sine wave with a random frequency in the range [½, 1] (i.e. capture somewhere between half and one period of the waveform over the domain [0,1]).
The two extremes for this are
Plot[Sin[ \[Pi] x], {x, 0, 1}]
and
Plot[Sin[2 \[Pi] x], {x, 0, 1}]
My initial effort for this was to replace the 2 with a call to RandomReal[{1, 2}], but this results in a different random value being used for every x.
Putting the call to RandomReal in a block has the same behavior:
Plot[Block[{m = RandomReal[{1, 2}]}, Sin[m \[Pi] x]], {x, 0, 1}]
How can I force Mathematica to only evaluate RandomReal once so I get a single clean sine wave out?
Show@Table[ With[{c = RandomReal[{1, 2}]}, Plot[Sin[c \[Pi] x], {x, 0, 1}]], 10]
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