Sound Level (trouble setting up equation)

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Increasing a sound source by 30 dB results in a specific increase in intensity, which can be calculated using the equation β2 = β1 + 30. The initial setup of the equations for sound level and intensity was incorrect, leading to confusion. The correct approach involves recognizing that the difference in sound levels corresponds to the logarithmic relationship of intensity. By applying properties of logarithms, the problem was resolved successfully. The discussion highlights the importance of correctly setting up equations in sound intensity calculations.
Saladsamurai
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Sound Level and Intensity (trouble setting up equation)

A certain sound source is increased by 30 dB. By what multiple is its intensity increased?

This is what I have set up so far, but I do not think it is correct..

\beta_1=10\log\frac{I_1}{I_0} and \beta_2=40\log\frac{I_1}{I_0}
So,
\frac{\beta_1}{\beta_2}=\frac{10\log\frac{I_1}{I_0}}{40\log\frac{I_1}{I_0}}

and from there I am jammed...we have been using product and sum logs so far...but this expression does not fit the bill..so I believe I have made a conceptual error in setting up the equation.

Do you see my error?
Casey
 
Last edited:
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This is killing me.

Edit: I think I found the correct relationship...how about beta2=beta1+30

so beta2-beta1=30...and then I should be able to use properties of Logs......that worked.

Sweeeeeeeet.
Casey
 
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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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