Amplitude of sum of waves with different frequencies

[imago]

Hi everybody, this is my first post here :P

I'm currently struggling over a weird problem, which asks for the amplitude (eg, max value) of a sum of many waves with different frequencies.

eg,
max value of
$\sum_0^N {A_i cos(w_i t + \phi_t)}$

 

[BruceW]

Welcome to the forum, imago :)

Usually in the homework section, people write in the given format, and give an attempt at the answer. But anyway, about the problem: did you mean phi_i instead of phi_t ? phi_i would make more sense, as the 'i'th wave's phase factor.

There are probably a few ways to get the answer to the question... What were your initial thoughts?

 

[olivermsun]

Hint: "with different frequencies"