Question

The two highest-pitch strings on a violin are tuned to 400 Hz (the A string) and 639 Hz (the E string). What is the ratio of the mass of the A string to that of the E string?

Answer 1

The ratio of the mass of the A string to that of the E string can be found by comparing their frequencies. The frequency of a string is inversely proportional to the square root of its linear mass density.

Step-by-step explanation:

The ratio of the mass of the A string to that of the E string can be found by comparing their frequencies. The frequency of a string is inversely proportional to the square root of its linear mass density. Since the linear mass density is directly proportional to the mass per unit length, we can say that the ratio of the mass of the A string to that of the E string is equal to the ratio of the square of their frequencies.

Given that the frequency of the A string is 400 Hz and the frequency of the E string is 639 Hz, the ratio of their masses can be calculated as follows:

Mass of A string / Mass of E string = (Frequency of A string)^2 / (Frequency of E string)^2

Mass of A string / Mass of E string = (400 Hz)^2 / (639 Hz)^2