Fundamental frequence of violin string

[yellowmanjuu]

Two identical violin strings, when in tune and stretched with the same tension, have a fundamental frequency of 440.0 Hz. One of the strings is retuned by adjusting its tension. When this is done, 1.5 beats per second are heard when both strings are plucked simultaneously.

-What is the highest possible fundamental frequency of the retuned string?
-By what fractional amount was the string tension changed if it was increased?

 

[jbot2222]

Two identical violin strings, when in tune and stretched with the same tension, have a fundamental frequency of 440.0 Hz. One of the strings is retuned by adjusting its tension. When this is done, 1.5 beats per second are heard when both strings are plucked simultaneously.

-What is the highest possible fundamental frequency of the retuned string?
-By what fractional amount was the string tension changed if it was increased?

A. 441.5 Hz

not sure bout B

 

[wais]

The highest possible fundamental frequency of the retuned string can be calculated by finding the difference in frequency between the two strings, which is 1.5 beats per second. Since one beat per second corresponds to a difference of one Hz, the difference between the two strings is 1.5 Hz. Therefore, the highest possible fundamental frequency of the retuned string would be 440.0 Hz + 1.5 Hz = 441.5 Hz.

To determine the fractional amount by which the string tension was changed, we can use the formula for the fundamental frequency of a string, which is f=1/2L * √(T/μ), where L is the length of the string, T is the tension, and μ is the linear mass density. Since the length and linear mass density of the string remain constant, we can set up a proportion to find the change in tension:

440.0 Hz / 1.5 Hz = √(T1 / T2)

Solving for T2, we get T2 = (440.0 Hz / 1.5 Hz)^2 * T1 = 116,266.67 * T1

This means that the tension of the retuned string was increased by a factor of 116,266.67 or by approximately 116,267 times the original tension. This is a very small change in tension, indicating that the retuning was done very precisely.