Our ears do not sense that the loudness of a sound increases in direct proportio

Question

Our ears do not sense that the loudness of a sound increases in direct proportion to the intensity or the sound level. For example, if the intensity of a sound doubles - we do not experience it as twice as loud. Rather if the intensity increases by ten times then we experience the sound as twice as loud. Similarly if the intensity increases by 100 (10^2) times then we perceive the sound to be 2^2 or 4 times louder. Using the information above, if the intensity of a sound increases by a factor of 10,calculate the change in the sound level. If the intensity of a sound goes up by a factor of 1000, calculate the change in the sound level and also the increase in loudness of the sound. A chicken farmer wants to increase the size of her flock of chickens from 500 to 2000. She wants to alieve her husband's concern that the four fold increase in chickens would mean that the 2000 chickens would be four times louder than 500. Knowing that four times more chickens would result in four times the intensity of the sound, calculate the difference in sound level. Approximately how much louder would this seem? Explain. How big can her flock become before it seems four times as loud?

Explanation / Answer

I = 10 log(I/Io)

I2 - I1 = 10log(10I/Io) - 10log(I/Io)

I2 - I1 = 10log(10I/I) = 10log(10) = 10 db

subpart b )

I2-I1 = 10log(1000) = 30 dB

part b )

new intensity = 4I

I2-I1 = 10log(4) = 6.02 dB

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