Answer :
Answer: The tension in the A string of the violin must be placed under 263.7 N of tension.
The A string on a violin has a fundamental frequency of a 440 Hz.
To find the tension (T) in a string: T = (m * v²) / L
Where: m = the mass of the string, L = the length of the vibrating portion, v = the speed of the wave. The speed of the wave is given by the formula: v = √(T/μ)
Where T is the tension in the string and μ is the linear density of the string. To calculate the linear density of the string, we use the formula: μ = m/L
Fundamental frequency, f = 440 Hz
Length of the vibrating portion, L = 30.4 cm = 0.304 m
Mass of the string, m = 0.342 g = 0.000342 kg.
Using the frequency and the length of the vibrating portion, we can find the speed of the wave:
v = f * λλ
= 2L = 2(0.304 m)
= 0.608 mv
= (440 Hz)(0.608 m)
= 267.52 m/s.
Now, we can find the tension in the string:
T = (m * v²) / L
T = (0.000342 kg * (267.52 m/s)²) / 0.304 m
T ≈ 263.7 N.
Therefore, the tension in the A string of the violin must be placed under 263.7 N of tension.
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