physics
posted by melissa .
A particular guitar string is supposed to vibrate at 210Hz , but it is measured to vibrate at 220Hz
By what percent should the tension in the string be changed to correct the frequency?

v=sqrt(T•L/m)
λ=v/f => f=v/λ= sqrt(T•L/m)/ λ
f₁/f₂={sqrt(T₁•L/m)/ λ}/{sqrt(T₂•L/m)/ λ}
(f₁/f₂)² =T₁/T₂
T₂=T₁(f₂/f₁)²
(T₂T₁)/T₁=(T₂/T₁) 1=(f₂/f₁)²1=(220/210)²1=0.0975.
=> 9.75%