Question

Suppose a certain jet plane creates an intensity level of 124 dB at a distance of 5.01 m. What intensity level does it create on the ground directly underneath it when flying at an altitude of 2.25 km?

Answer 1

Answer:71 dB

Step-by-step explanation:

Given

sound Level
`\beta _1=124 dB`

distance
`r_1=5.01 m`

From sound Intensity

`\beta =10dB\log ((I_1)/(I_0))`

`124=10dB\log ((I_1)/(I_0))`

`12.4=\log ((I_1)/(I_0))`

`I_1=(1* 10^(-12))* 10^(12.4)`

`I_1=2.51 W/m^2`

we know Intensity
`I\propto ^(1)/(r^2)`

`I_1r_1^2=I_2r_2^2`

`I_2=I_1((r_1)/(r_2))^2`

`I_2=2.51\cdot ((5.01)/(2.25* 10^3))^2`

`I_2=1.24* 10^(-5) W/m^2`

Sound level corresponding to
`I_2`

`\beta _2=10\log ((I_2)/(I_0))`

`\beta _2=10\log ((1.24* 10^(-5))/(1* 10^(-12)))`

`\beta _2=70.93\approx 71 dB`