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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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Most popular questions from this chapter

How fast (as a percentage of light speed) would a star have to be moving so that the frequency of the light we receive from it is 10.0% higher than the frequency of the light it is emitting? Would it be moving away from us or toward us? (Assume it is moving either directly away from us or directly toward us.)

Two organ pipes, open at one end but closed at the other, are each 1.14m long. One is now lengthened by 2.00 cm . Find the beat frequency that they produce when playing together in their fundamentals.

In case 1, a source of sound approaches a stationary observer at speed u. In case 2, the observer moves toward the stationary source at the same speed u. If the source is always producing the same frequency sound, will the observer hear the same frequency in both cases, since the relative speed is the same each time? Why or why not?

(a) A sound source producing 1.00-kHz waves moves toward a stationary listener at one-half the speed of sound. What frequency will the listener hear? (b) Suppose instead that the source is stationary and the listener moves toward the source at one-half the speed of sound. What frequency does the listener hear? How does your answer compare to that in part (a)? Explain on physical grounds why the two answers differ.

A jet plane flies overhead at Mach 1.70 and at a constant altitude of 1250 m. (a) What is the angle σof the shock-wave cone? (b) How much time after the plane passes directly overhead do you hear the sonic boom? Neglect the variation of the speed of sound with altitude.
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