At a distance of 10.0 m, the humming noise of a single NewJersey mosquito is nea

Question

At a distance of 10.0 m, the humming noise of a single NewJersey mosquito is near the threshold of human hearing (0.000dB). Suppose that 1000 such NJ mosquitoes are gathered in acompact swarm 10.0 m away. A) Please state the sound intensity level due to theswarm. B) How far from the swarm would a listener need to stand inorder to reduce the mosquito noise back to the 0.000 dB thersholdlevel? At a distance of 10.0 m, the humming noise of a single NewJersey mosquito is near the threshold of human hearing (0.000dB). Suppose that 1000 such NJ mosquitoes are gathered in acompact swarm 10.0 m away. A) Please state the sound intensity level due to theswarm. B) How far from the swarm would a listener need to stand inorder to reduce the mosquito noise back to the 0.000 dB thersholdlevel?

Explanation / Answer

Sound level = 10*log(I/Io) where I is the intensity of sound at the given point, and Io is thereference intensity. Clearly, I = 1000*Io The swarm is producing sound at an intensity I, and we know that interference of the sound waves leads to anintensity of : I = Io*(1000)2 Since the amplitudes are added to give A = 1000Ao and I A2 So, new sound level would be 10*log(1000000) = 60 dB Also, we know that I 1/r2 since the total powertransmitted through the area 4r2 from the source to a point at distance 'r' remains constant for all'r'. So, for I' = Io, (A'/r')2 = (Ao/r)2 But A' = 1000Ao and r = 10m So, r' = 100 m

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