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):
tanϕ=43ϕ=tan-14/3
Step 2:Findtheamplitudeoftheresultantwave.
Also,a2cos2ϕ+a2sin2ϕ=32+42
a2(cos2ϕ+sin2ϕ)=25
a2.1=25a=5
Hence,y=5cosϕsinωt+5sinϕcosωt
=5[cosϕsinωt+sinϕcosωt]=5sin(ωt+ϕ)
whereϕ=tan-14/3
Hence,amplitude=5cm