Lowest frequency that produces an interference maximum

AI Thread Summary
To determine the lowest frequency that produces an interference maximum at the microphone's location, the distances from the speakers to the microphone must be calculated. The equation r2 - r1 = (n - 0.5)(lambda) is used, where lambda is derived from the wave speed divided by frequency. The speaker separation and microphone distance are essential for finding the values of r1 and r2. The user initially struggled with determining the appropriate value for n but later resolved the issue. The discussion emphasizes the application of wave interference principles to solve for frequency.
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Homework Statement



A microphone is located on the line connecting two speakers that are 0.517 m apart and oscillating 180° out of phase. The microphone is 1.96 m from the midpoint of the two speakers. What is the lowest frequency that produces an interference maximum at the microphone's location?

What is the next lowest frequency that produces an interference maximum at the microphone's location?



Homework Equations



r2 -r1 = (n-0.5)(lambda)
lambda=v/f
v=343m/s

The Attempt at a Solution



r2 and r1 are the distances from the speaker
so r2 is .517/2 + 1.96 = 2.2185
and r1 is .517/2 + 2.2185 = 2.477

i know i have to solve for frequency so i plugged (343m/s)/f into the equation

but then i got stuck. what do i plug in for n and how i change n for the lowest frequency and the next lowest?
 
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nevermind, figured it out

DISREGARD THE QUESTION!
 
Can you please tell me how to do this one? I've tried by using the equations but still can not figure it out.
Thanks!
 
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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