The displacement of an elastic wave is given by the function y=3sinωt+4cosωt, where y is in cm and t is in seconds. Calculate the resultant amplitude.

Hint: Use the concept of superposition of waves.
Step 1: Find the phase of the resultant wave.
Given, displacement of an elastic wave, y=3sinωt+4cosωt,
Assume,                                           3=acosϕ                                          .....(i)
4=asinϕ                                           .....(ii) 
On dividing Eq. (ii) by Eq. (i):
Step 2: Find the amplitude of the resultant wave.
Also,                         a2cos2ϕ+a2sin2ϕ=32+42
                                                  a2 .1 =25a=5
Hence,                                              y=5cosϕsinωt +5sinϕcosωt
                                                          =5[cosϕsinωt+sinϕcosωt ]=5 sin(ωt+ϕ)
where                                                ϕ=tan-14/3
Hence, amplitude=5cm