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Posted by on Thursday, December 13, 2012 at 12:24pm.

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?

  • physics - , Thursday, December 13, 2012 at 12:49pm

    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
    (T₂-T₁)/T₁=(T₂/T₁) -1=(f₂/f₁)²-1=(220/210)²-1=0.0975.
    => 9.75%

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