To determine how many buzzing mosquitoes it would take to reach a sound level of a normal conversation, we can use the fact that sound intensity (in decibels) is logarithmic and can be expressed as:
dB = 10 log(I/I₀)
where I is the sound intensity of the source, I₀ is a reference sound intensity (usually taken to be the threshold of human hearing, which is 1 x 10^-12 W/m^2), and dB is the sound level in decibels.
If we rearrange this equation to solve for I, we get:
I = I₀ 10^(dB/10)
Now, we can use this equation to calculate the sound intensity of one buzzing mosquito, given that its sound level is 40 dB:
I₁ = I₀ 10^(40/10) = I₀ 10^4
Similarly, we can calculate the sound intensity of a normal conversation, given that its sound level is 50 dB:
I₂ = I₀ 10^(50/10) = I₀ 10^5
To find how many mosquitoes it would take to produce the same sound intensity as a normal conversation, we can divide I₂ by I₁:
n = I₂ / I₁ = (I₀ 10^5) / (I₀ 10^4) = 10
So, it would take approximately 10 buzzing mosquitoes to produce the same sound intensity as a normal conversation.