How Does Beat Frequency Help Tune a Violin to Concert A?

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AI Thread Summary
The discussion centers on a violinist tuning her instrument to concert A (440 Hz) and experiencing a beat frequency of 3 Hz, which increases to 4 Hz when the string is tightened. The calculated frequency of the violin when the 3 Hz beat was heard is 443 Hz, but the teacher's posted solution is 433 Hz, suggesting a possible typo. Participants agree that to achieve perfect tuning, the violin string should be loosened, as reducing tension lowers the frequency. The term "slightly" indicates that minor adjustments are necessary for accurate tuning. The conversation highlights the importance of understanding beat frequencies in tuning musical instruments.
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Homework Statement


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 3Hz, which increases to 4Hz when she tightens her violin string slightly. (a) what was the frequency of her violin when she heard the 3Hz beat? (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 3Hz beat?


Homework Equations


f beat= f1-f2




The Attempt at a Solution



F2= fbeat+f1 F2= 3Hz + 440Hz F2= 443Hz

The teacher has posted the solution to be 433Hz. Did he just make a typo, or am I doing something wrong?
 
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Typo. Obvious typo.
 
part b is confusing me. I would think that you would loosen the tension which would slow down the velocity which would reduce the frequency?
 
I would agree with you. Why would you doubt it? I think the key word here is 'slightly'.
 
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Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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