What Is the Vibrational Frequency of a Guitar String Based on Beat Frequencies?

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AI Thread Summary
The discussion centers on determining the vibrational frequency of a guitar string based on beat frequencies produced when sounded with two different tuning forks. The string generates 4 beats per second with a 350-Hz fork and 9 beats per second with a 355-Hz fork. To solve the problem, participants are encouraged to use the relationship between beat frequency and the difference in frequencies of the two sounds. The relevant equation involves understanding that the beat frequency equals the absolute difference between the frequencies of the two sources. The thread seeks clarification on how to apply these concepts to find the string's frequency.
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Homework Statement


A guitar string produces 4 beat/s when sounded with a 350-Hz tuning fork and 9 beat/s when sounded with a 355-Hz fork. What is the vibrational frequency of the string? Explain your reasoning.


Homework Equations


f=v//\


The Attempt at a Solution


I'm not quite sure how to start solving this problem. I know that frequency is velocity divided by wavelength. What equation or equations that have beat/s as variables could I use to solve this problem?
 
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Thread 'Variable mass system : water sprayed into a moving container'

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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