SOLUTION: The acoustical intensity, I, of a sound wave is proportional to the square of the pressure amplitude, P, and inversely proportional to the velocity, v, of the wave. If I=0.6W/m^2 f

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The acoustical intensity, I, of a sound wave is proportional to the square of the pressure amplitude, P, and inversely proportional to the velocity, v, of the wave. If I=0.6W/m^2 f      Log On


   

Question 436849: The acoustical intensity, I, of a sound wave is proportional to the square of the pressure amplitude, P, and inversely proportional to the velocity, v, of the wave. If I=0.6W/m^2 for P=30.0Pa and v=150m/s, find v if P=50 Pa and I=2.4W/m^2.
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Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The acoustical intensity, I, of a sound wave is proportional to the square of
the pressure amplitude, P, and inversely proportional to the velocity, v, of the wave.
If I=0.6W/m^2 for P=30.0Pa and v=150m/s, find v if P=50 Pa and I=2.4W/m^2.
:
From the given information we can write a formula:
I = %28k%2Ap%5E2%29%2Fv, where k is the constant of variation
:
Using the given values, find k:
"If I=0.6W/m^2 for P=30.0Pa and v=150m/s
:
.6 = %28k%2A30%5E2%29%2F150
150*.6 = 900k
90 = 900k
k = 90%2F900
k = .1 the constant of variation
:
We can write the formula
I = %28.1p%5E2%29%2Fv
:
"find v if P=50 Pa and I=2.4W/m^2."
2.4 = %28.1%2A50%5E2%29%2Fv
2.4v = .1*2500
v = 250%2F2.4
v = 104.167 m/sec