Answer :
The ratio of the linear mass density of the highest string to that of the next highest string is 1.5:1.
The strings on a violin have the same length and approximately the same tension.
If the highest string has a frequency of 659 Hz, and the next highest has a frequency of 440 Hz, the ratio of the linear mass density of the highest string to that of the next highest string is 1.5:1.
The ratio of the linear mass density of the highest string to that of the next highest string can be calculated as follows:
The frequency of a string vibrating in a particular mode is directly proportional to the tension in the string and inversely proportional to the string's linear mass density.
The higher the frequency of the string, the lower the linear mass density of the string.
The formula for the frequency of a vibrating string is:
f = (1/2L) * √(T/μ)where L is the length of the string, T is the tension in the string, and μ is the linear mass density of the string.
To find the ratio of the linear mass density of the highest string to that of the next highest string, we can use this formula to find the linear mass density ratio.
We can write the formula for the two strings and divide one by the other to get a ratio of
μ1/μ2:659 Hz = (1/2L) * √(T/μ1)440 Hz
= (1/2L) * √(T/μ2)659/440
= √(μ2/μ1)1.5
= μ1/μ2
So the ratio of the linear mass density of the highest string to that of the next highest string is 1.5:1.
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