Question

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

Answer 1

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

Step-by-step 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