Sarahisme Posted September 23, 2005 Share Posted September 23, 2005 [math] m = 0.1g = 0.1 \times 10^{-3} kg [/math] [math] \Delta t = 0.1 s [/math] PE of ball = [math] (0.1 \times 10^{-3} kg)(9.81 ms^{-2})(1m) [/math] but only 0.05% of it is converted into a sound wave so : Energy (E) = [math] (0.0005)(0.1 \times 10^{-3} kg)(9.81 ms^{-2})(1m) [/math] Now Power is Energy per unit time, so Power (P) is: [math] E = \frac{(0.0005)(0.1 \times 10^{-3} kg)(9.81 ms^{-2})(1m)}{0.1s} [/math] Intensity is Power per unit area (since it can be approimated to a point source of sound the area is the surface area of a sphere, [math] 4 \pi r^2 [/math], so Intensity is : [math] I = \frac{(0.0005)(0.1 \times 10^{-3} kg)(9.81 ms^{-2})(1m)}{(0.1s)(4 \pi r^2)} [/math] Since we are given that the lowest audible intensity is [math] 10^{-11} Wm^{-2} [/math] then we set I = [math] 10^{-11} Wm^{-2} [/math] so we have: [math] \frac{(0.0005)(0.1 \times 10^{-3} kg)(9.81 ms^{-2})(1m)}{(0.1s)(4 \pi r^2)} = 10^{-11} Wm^{-2} [/math] So then rearranging and solving for r gives: r = 200 m ( to 1 sig. fig.) now for part (b) we just set I = [math] 10^{-8} Wm^{-2} [/math] instead, so we have : [math] \frac{(0.0005)(0.1 \times 10^{-3} kg)(9.81 ms^{-2})(1m)}{(0.1s)(4 \pi r^2)} = 10^{-8} Wm^{-2} [/math] now rearraging for r gives : r = 6 m (to 1 sig. fig.) Link to comment Share on other sites More sharing options...
Sarahisme Posted September 23, 2005 Author Share Posted September 23, 2005 oh yeah, i just wanted to know if i had done things correctly? :S Link to comment Share on other sites More sharing options...
Sarahisme Posted September 25, 2005 Author Share Posted September 25, 2005 hello? Link to comment Share on other sites More sharing options...
mezarashi Posted September 25, 2005 Share Posted September 25, 2005 Your approach seems good enough ^^. Should be okay. Link to comment Share on other sites More sharing options...
Sarahisme Posted September 26, 2005 Author Share Posted September 26, 2005 right ok, thanks Link to comment Share on other sites More sharing options...
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