Understanding the Amplitude of sin2x

[Apurv Zoad]

If we look at the graph of sin2x, well its Time Period is pi, and amplitude is same as that of sinx. But if we expand sin2x as 2sinxcosx, rewriting it as 2cosxsinx. According to the Physics in SHM, Wave Motion, whatever is infront of sinx is called as Amplitude. Now, y = 2cosxsinx = Asinx, then why did Amplitude rise by A times, that is by 2cosx times ? I think that the cosx is the decreasing function, that's why the Amplitude must remain same !

 

[PeroK]

The amplitude ##A## must be a constant. ##\cos x## changes with ##x## so isn't an amplitude.

 

[hilbert2]

Only if one has two trigonometric functions, say ##\sin(k_1 x+b_1)## and ##\sin(k_2 x + b_2)##, that have wavenumbers of very different magnitudes, ##k_2 >> k_1## we can call a factor of ##\sin(k_1 x+b_1)## in front of ##\sin(k_2 x + b_2)## an "amplitude" because of the phenomenon of beats. If ##k_1## and ##k_2## are of same order of magnitude, this is not appropriate.