The two highest-pitched strings on a violin are tuned to 440 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? Assume that the violin strings are all the same length and under essentially the same tension.

Question

High School

Answer :

adefunkeadewole adefunkeadewole · Answer 1 · 2024-11-16T04:57:28-05:00

the ratio of the mass of the A string to that of the E string is 0.653.

the equation for the frequency of a vibrating string is given as :

f = (1/2L) * √(T/μ)

f_ = frequency of the string,

L= length of the string,

T= tension in the string, and

μ= linear mass density of the string

We know that the strings are all the same length and under essentially the same tension,

f1/√μ1 = f2/√μ2

f1= frequency of the A string,

μ1 = linear mass density of the A string,

f2= frequency of the E string, and

μ2= linear mass density of the E string.

440/√(m1/L) = 639/√(m2/L)

440/√m1 = 639/√m2

(440 * √m2)² = (639 * √m1)²

m2 = (639/440)² * m1

In conclusion, we have that the ratio of the mass of the A string to that of the E string is:

m1/m2 = 1/[(639/440)²]

m1/m = 0.653

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