Intensity of periodic sound waves

AI Thread Summary
To determine the sound level at 4.00 km from the firework explosion, the acoustic pressure of 10.0 N/m² is used to calculate the intensity using the formula I = (deltaPmax)²/(2pv), where p is the density of air and v is the speed of sound. The intensity is then converted to decibels using B(dB) = 10 log(I/I₀), with I₀ being the reference intensity. Additionally, the sound absorption rate of 7.0 dB/km must be factored in for the distance of 4.00 km, leading to a total reduction in sound level. The final calculated sound level is 65.6 dB at that distance.
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Homework Statement


A firework charge is detonated many meters above the ground. At a distance of 400m from the explosion, the acoustic pressure reaches a maximum of 10.0 N/m2. Assume that the speed of sound is constant at 343 m/s throughout the atmosphere over the region considered, that the ground absorbs all the sound falling on it, and that the air absorbs sound energy as described by the rate 7.0 dB/km.

What is the sound level (dB) at 4.00km from the explosion?



Homework Equations




B(dB)=10log(I/Io); I=(deltaPmax)^2/(2pv)=Power/Area


The Attempt at a Solution



I plug the data into the equations but it give me the wrong answer. I don t know why the answer is 65.6dB. Especially how to use the acoustics pressure?
 
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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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