physics
posted by ashlee .
The string on a violin has a fundamental frequency of 120.0 Hz. The length of the vibrating portion is 36 cm and has a mass of 0.58 g. Under what tension (in newtons) must the string be placed?

The fundamental frequency is: f1 = 120Hz
At the fundamental, the string has two nodes at the end, and one antinode in the middle, so therefore the vibrating length of the string (0.36 m) is equal to λ/2 , so λ= 0.72 m.
v = λ•f = 0.72• 120 = 86.4 m/s.
Now we will apply the wave speed in a string relationship, which is:
v = sqrt(T/mₒ),
where mₒ = m/L= 0.58•10^3/0.36 = 1.6•10^3 kg/m is mass/length for the cord,
and T is the tension in the cord.
Therefore, T = mₒ•v² =1.6•10^3 •(86.4)² ≈ 12 N.
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