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Chapter 2: Q41E (page 541)

A violinist is tuning her instrument to concert A (440鈥�Hz). She plays the note while listening to an electronically generated tone of exactly that frequency and hears a beat frequency of 3鈥�Hz, which increases to 4鈥�Hzwhen she tightens her violin string slightly. (a) What was the frequency of the note played by her violin when she heard the3鈥�Hz beats? (b) To get her violin perfectly tuned to concert A, should she tighten or loosen her string from what it was when she heard the 3鈥�Hzbeats?

Short Answer

Expert verified

(a) The frequency of the violin isfv=443鈥塇锄

(b) For perfect tuning, the violinist should loosen the string.

Step by step solution

01

Beat frequency formula

The beat frequency is the difference in frequency of the superimposed waves fbeat=|f1-f2| .

Since, we have violin and electrically generate frequency, we will have

role="math" localid="1655811690524" fbeat=fv鈭�fefv=fbeat+fe

02

Calculate the violin frequency

Given that fbeat=3鈥塇锄and fe=440鈥塇锄.

fv=fbeat+fefv=3鈥嬧�嬧�塇锄+440鈥塇锄fv=443鈥塇锄

03

Make beat frequency equal to zero

In order to get her violin perfectly tuned, the beat frequency must be zero. This means that fv should decrease by 3鈥塇锄. To decrease the frequency, the violinist should loosen the string.

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