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Chapter 17: Q10. (page 483)

The two highest-pitch strings on a violin are tuned to 440 Hz (the A string) and 659 Hz (the E string). What is the ratio of the mass of the A string to that of the E string? Violin strings are all the same length and under essentially the same tension.

Short Answer

Expert verified

1 : 2.243

Step by step solution

01

Given parameters

Two strings of same length and tension but different masses and different fundamental frequencies.

Frequencies are: 659Hz and 440Hz.

02

Applying the formula

f=12LTs渭

03

Taking ratio

f1=12LTs渭1f2=12LTs渭2f1f2=渭2渭1f1f2=m2m14406592=m2m10.445=m2m1m1m2=2.243m1:m2=1:2.243

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