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Oscillations

# The wave equation of 2 waves are given by $\;x_{1}=4 sin 3t\; mts\;$ and $\;x_{2}=3 cos 3t \;mts \;.$ The amplitude of the resulting wave is

$(a)\;5\;mts\qquad(b)\;6\;mts\qquad(c)\;7\;mts\qquad(d)\;1\;mts$

Answer : (a) $\;5\; mts$
Explanation :
The final wave is given by
$4 sin 3t +3 cos 3t = 5 \;(\large\frac{4}{5}\;sin 3t + \large\frac{3}{5} \;cos 3t)$
$=5 \;sin(3t+sin^{-1}(\large\frac{3}{5}))$
Therefore , wave amplitude is 5 mts .