The displacement of a particle is given by $x = 3\sin (5\pi \,t) + 4\cos (5\pi \,t)$The amplitude of the particle is
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(c) For the given super imposing waves
${a_1} = 3,$ ${a_2} = 4$ and phase difference $\phi = \frac{\pi }{2}$
==> $A = \sqrt {a_1^2 + a_2^2 + 2{a_1}{a_2}\cos \pi /2} = \sqrt {{{(3)}^2} + {{(4)}^2}} = 5$
${a_1} = 3,$ ${a_2} = 4$ and phase difference $\phi = \frac{\pi }{2}$
==> $A = \sqrt {a_1^2 + a_2^2 + 2{a_1}{a_2}\cos \pi /2} = \sqrt {{{(3)}^2} + {{(4)}^2}} = 5$
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