A jet plane at takeoff can produce sound of intensity 10.0 W/m2 at 30.0 m away. But you prefer the tranquil sound of normal conversation, which is 1.0 m W/m2. Assume that the plane behaves like a point source of sound. (a) What is the closest distance you should live from the airport runway to preserve your peace of mind? (b) What intensity from the jet does your friend experience if she lives twice as far from the runway as you do? (c) What power of sound does the jet produce at takeoff?

Solution 25E Step 1 of 6: (a) What is the closest distance you should live from the airport runway to preserve your peace of mind Intensity of jet plane sound , I =11 W/m at distance r =30 m 1 2 6 2 Intensity of jet plane sound , I =12 W/m =1× 10 W/m at distance r = 2 Using the inverse square law, 2 I1 r2 2 = r2 1 Solving for r , 2 2 I1 2 r 2 I2r1 I r = r 1 2 1 I2 Step 2 of 6: Substituting I =10 W/m , r =30 m, I =1× 10 W/m 6 2 1 1 2 10 W/m2 r2= 30 m 1×10 W/m 2 3 r2= 95 × 10 m 3 Using 1km=10 m r2= 95km Therefore, the closest distance you should live from the airport runway to preserve your peace of mind is 95 km. Step 3 of 6: (b) What intensity from the jet does your friend experience if she lives twice as far from the runway as you do Intensity of jet plane sound , I =101W/m at distance r =30 m 1 3 3 Intensity of jet plane sound , I = 2t distance r =2(95× 20 m)=180× 10 m Using the inverse square law, r2 I1 = 2 I2 r1 Solving for I , 2 r2 I = 1 I 2 r2 1