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Caculating the tention, max accaleration and velocity of a violin string

  1. Dec 16, 2009 #1
    1. The problem statement, all variables and given/known data

    String on the violin is made of steel wire with a diameter of 0.25 mm. With what force must the string be strained (stretched) so that its basic frequency will equal 660 Hz (E-string)? What is the maximum velocity and acceleration of the parts of the string, if we evoke basic vibration with amplitude of 5 mm? In the rest, the fastened string is long l = 325 mm, the density of steel is 7800 kg/m3.

    2. Relevant equations

    μ= m/L
    v= 2Lf
    a(max)= ω²A

    3. The attempt at a solution

    First part: With what force must the string be strained so that its basic frequency will equal 660 Hz (E-string)?

    Volume of cylinder: V= πr²h= π(1/d)²L= 16 x 10^-9 m³, ρ= 7800 kg/m³
    Mass of the string: m= Vρ= 0.00013 kg
    Linear mass density: μ= m/L (kg/m)→ μ= 0.0004 kg/m

    v= 2Lf= 2(0.325m)(660 hz)= 429 m/s
    v= sqrt(T/ μ) → T or F= μv²
    F= 73.61 N

    Second part: What is the maximum velocity and acceleration of the parts of the string, if we evoke basic vibration with amplitude of 5 mm?

    v= 2Lf= 2(0.325m)(660 hz)= 429 m/s
    a(max)= ω²A= (2πf)²A= 85897m/s²
     
  2. jcsd
  3. Dec 16, 2009 #2
    Looks right to me.
     
  4. Dec 16, 2009 #3
    Thank you.
     
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