Answer:
Amplitude changes by factor of 2 means double.
Explanation:
Given:
If the power delivered to the string is quadrupled.
From the formula of power transmitted by a sinusoidal wave on a stretched string is,
[tex]P = \frac{1}{2} \mu \omega ^{2} A^{2} v[/tex]
Where [tex]\mu =[/tex] mass per unit length, [tex]\omega =[/tex] angular speed, [tex]A =[/tex] amplitude, [tex]v =[/tex] wave speed, [tex]P =[/tex] power delivered.
Here we need only two terms power and amplitude.
[tex]P[/tex]∝ [tex]A^{2}[/tex]
All other quantities are constant for our problem,
[tex]A = k \sqrt{P}[/tex]
Where [tex]k =[/tex] constant
Here Power become quadruple means four times,
[tex]A = \sqrt{4P}[/tex]
[tex]A = 2\sqrt{P}[/tex]
So amplitude changes by factor of 2 means double
