Finding the possible frequencies of a tuning fork

AI Thread Summary
The discussion revolves around calculating the possible frequencies of a tuning fork based on a vibrating wire's properties. The wire, with a mass of 0.0120 kg and a length of 2.05 m, vibrates under a tension of 202 N, yielding a fundamental frequency. A beat frequency of 5.10 Hz indicates that the tuning fork's frequency is close to the wire's frequency. Participants suggest using the beat frequency equation to find the two possible frequencies of the tuning fork, which should be calculated as the wire's frequency plus and minus the beat frequency. The correct approach involves determining the wire's frequency first and then applying the beat frequency to find the tuning fork's frequencies.
chris097
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Homework Statement



A 0.0120 kg, 2.05 m long wire is fixed at both ends and vibrates in its simplest mode under a tension of 202 N. When a tuning fork is placed near the wire, a beat frequency of 5.10 Hz is heard. What are the possible frequencies of the tuning fork? (enter the smaller frequency first) (It asks for 2 answers)


Homework Equations



f = √(TL/m)/2L
fb = |f1 - f2|


The Attempt at a Solution



I first found the frequency of the string using equation 1 then I simply thought that the frequency of the tuning fork would always be multiples of 5.10 Hz from the frequency of the fork. So i got answers like 50.4, 50.5...


Can anyone please help out?
Thanks!
 
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Just use the second equation you listed in section 2. you know f_b and f_1 so what can f_2 be?
 
willem2 said:
Just use the second equation you listed in section 2. you know f_b and f_1 so what can f_2 be?

I end up getting 50.4 and 55.5 Hz, which is wrong.
 
f - 5.1 and f + 5.1
 
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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