The displacement of an elastic wave is given

Given,

y = 3 sin ωt + 4 cos ωt

Let’s consider

3 = a cos φ

4 = a sin φ

Then

y = a cos φ ωt + a sin φ ωt

y = a sin (ωt + φ)

tan φ = 4/3

φ = tan-1 4/3

When the above equation is squared, we het

a2 = 25

a = 5

Therefore, the new amplitude is 5 cm.