Two strings on a violin are stretched between two points 20.0 cm apart. The mass per length of the strings are the same. If the ratio of the frequencies of the fundamental modes is 1.5 to 1.0, then what is the ratio of the tensions in the strings?
Question
Two strings on a violin are stretched between two points 20.0 cm apart. The mass per length of the strings are the same. If the ratio of the frequencies of the fundamental modes is 1.5 to 1.0, then what is the ratio of the tensions in the strings?
Solution
The frequency of a vibrating string can be given by the formula:
f = (1/2L) * sqrt(T/u)
where: f is the frequency, L is the length of the string, T is the tension in the string, and u is the linear density (mass per length) of the string.
Given that the lengths and the linear densities of the two strings are the same, the ratio of the frequencies of the two strings (f1/f2) is equal to the square root of the ratio of the tensions in the two strings (T1/T2).
So, if f1/f2 = 1.5/1.0 = 1.5, then sqrt(T1/T2) = 1.5.
Squaring both sides to solve for T1/T2, we get:
T1/T2 = (1.5)^2 = 2.25.
So, the ratio of the tensions in the two strings is 2.25 to 1.
Similar Questions
A string on a violin is stretched between two points 20.00 cm apart with a tension of 120.0 N. The mass/length of the string is 0.002000 kg/m. The frequency of the mode next higher than the fundamental mode is
A string with a mass/length of 0.00200 kg/m is stretched between two points with a tension of 120 N. If the fundamental frequency is 440 Hz, then what is the distance between the two points?
A string on a guitar is stretched between two points 30.0 cm apart with a tension of 100 N. The mass/length of the string is 0.003 kg/m. The wavelength of the mode of vibration with the lowest frequency is
the length radius tension and density of string A are twice the same parameters of string B gind the ratio of fundamental frequency of B to the fundamental frequencey of A if both ends of each wire is fixed
Determine the tension in the string connecting the 2.00 kg and 1.00 kg masses.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.