A source vibrating at constant frequency generates a sinusoidal wave on a string under constant tension. If the power delivered to the string is tripled, by what factor does the amplitude change

n = 1,732    the amplitude must be increased by a factor of 1,732

Explanation:

The power delivered by a wave is given by

                  P = E / t

                  P = ½ μ w² v A²

let's apply this expression to our case the power tripled

                3P₀ = ½ μ w² v A’²

let's write the amplitude function of a initial amplitude

               A ’= n A₀

where n is a number

               3 P₀ = (½ μy w² v  A₀²) n²

               3P₀ = P₀ n²

               n = √ 3

               n = 1,732

therefore the amplitude must be increased by a factor of 1,732

a displacement distance is size of displ