What Is the Formula That Links Sound Wave Power and Frequency?

AI Thread Summary
The discussion centers on the formula linking sound wave power and frequency, specifically questioning if it excludes intensity and relies solely on wave amplitude. The provided equation for power from a spherical source in the far field is presented, highlighting its dependence on the root mean square pressure (p_rms), density (ρ_o), and speed of sound (c). Participants seek clarification on the derivation of this equation and its implications for understanding sound wave behavior. The conversation emphasizes the relationship between power, frequency, and the physical properties of sound waves. Overall, the thread aims to deepen the understanding of sound wave dynamics through mathematical exploration.
Werg22
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Was the formula tha links power and frequency (a formula that dosen't include intensity)?
 
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Wouldn't it just be the amplitude of the wave?
 
Power from a spherical source, is defined, in the far field as:

\Pi = \frac{4 \pi r^2 p^2_{rms}}{\rho_o c}
 
FredGarvin said:
Power from a spherical source, is defined, in the far field as:

\Pi = \frac{4 \pi r^2 p^2_{rms}}{\rho_o c}

How do you derive this equation? 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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