Two master violin players are playing violins by Stradivarius and Guarnieri. The

Question

Two master violin players are playing violins by Stradivarius and Guarnieri. The vibrating section of the A-string on both instruments is exactly 327 mm long. The A-strings on each instrument are identical with a mass density of 0.00078 kg/m. The player of the Stradivarius carefully tunes the A-string of her instrument to A-440 (440 Hz) using a pitch fork.
(a) What is the tension in the A-string of the Stradivarius?
N
(b) When the players play both A-strings together they notice that the Guaneri is at a slightly higher frequency. A beat frequency of 3 Hz is observed. What is the frequency of vibration of the A-string of the Guarnieri violin?
Hz

(c) What is the tension in the A-string of the Guarnieri violin?
N

Explanation / Answer

(a) Starting with:

v=f(2L) and v=(T/)

we find:

T=4f2L2

T=4(.00078)(4402)(.3272)

T=64.59 N

(b) the beat frequency is the difference between the two frequenecy, since we know the Guarnieri is higher we can simply add the beat frequency (3) to the frequency of the Stradivarius (440)

fG=443 Hz

(c) We can use the expression in A, but put the new frequency in (443)

T=4f2L2

T=4(.00078)(4432)(.3272)

T=65.47 N

hope that helps

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