If one doubles the tension in a violin string, the fundamental frequency of that string will increase by a factor of:
2
4
1.4
1.7
?_?
1.414, to be more exact. (The square root of 2)
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frequency is proportional to sqrt Tension
The fundamental frequency of a vibrating string is inversely proportional to the square root of the tension in the string. Therefore, if one doubles the tension in a violin string, the fundamental frequency of that string will increase by a factor of √2, which is approximately 1.4.
So the correct answer is 1.4.
To find the factor by which the fundamental frequency of a violin string increases when the tension is doubled, we need to understand the relationship between tension and fundamental frequency.
The fundamental frequency of a vibrating string is given by the equation:
f = (1/2L) * sqrt(T/μ)
Where:
f = fundamental frequency
L = length of the string
T = tension in the string
μ = linear density of the string
According to this equation, the fundamental frequency is directly proportional to the square root of the tension. In other words, if we double the tension (2T), the fundamental frequency (f) will increase by a factor of sqrt(2).
Therefore, the correct answer is:
1.4 (approximately)
It is important to note that this answer assumes all other variables, such as the length and density of the string, remain constant.