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Chapter 2: Q41E (page 541)

A violinist is tuning her instrument to concert A (440 Hz). She plays the note while listening to an electronically generated tone of exactly that frequency and hears a beat frequency of 3 Hz, which increases to 4 Hzwhen she tightens her violin string slightly. (a) What was the frequency of the note played by her violin when she heard the3 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 Hzbeats?

Short Answer

Expert verified

(a) The frequency of the violin isfv=443 Hz

(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−fefv=fbeat+fe

02

Calculate the violin frequency

Given that fbeat=3 Hzand fe=440 Hz.

fv=fbeat+fefv=3​​ Hz+440 Hzfv=443 Hz

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 Hz. To decrease the frequency, the violinist should loosen the string.

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