Please show all the work. Thank you! An endangered bird produces a call of sound

Question

Please show all the work. Thank you!

An endangered bird produces a call of sound intensity level 90.0dB re 1 x 10-12 w/m2 at a distance of 1.00 m. (The reference level is lo = 1 x 10 12 w/m2. All sould intensity levels in this problem use this same reference level.) This species of bird can detect calls at 45.0dB or louder in a quiet environment, but in a noisy environment, the calls must be exceed the background noise by 5.0 dB to be detected by the bird. 1. Find the intensity of the bird call at 1.00 m from the calling bird (where it has a sound intensity level of 90.0dB) and the intensity of the a call that is 45.0 dB (the quietest call the bird can hear in a quiet environment). 2. Assuming the sound of the bird call spreads spherically, what is the maximum distance away the bird can hear the call of another bird? 3. If there is traffic noise at sound intensity level 60.0 dB in the bird's habitat, find the intensity of the quietest call the bird can detect in this noisy environment. 4. Assuming the sound of the bird call spreads spherically, what is the maximum distance awa the bird can hear the call of another bird in the noisy environment. Note: This type of noise pollution is called masking, and it is a serious problem for animals that use sound to find a mate, detect predators, or find food because it decreases their detection area. The detection area is approximately a circle with radius equal to the maximum detection distance, so the detection area is proportional to the square of the maximum detection distance.

Explanation / Answer

1. SL = 10 log (I / I0 )

I0 = 10^-12 W/m^2

90 = 10 log (I / 10^-12)

I = 1 x 10^-3 W/m^2 . .....Ans

for 45 = 10 log(I / 10^-12)

I = 3.16 x 10^-8 W/m^2 ........Ans

2. P = I (4 pi r^2)

so I r^2 = constant

(1 x 10^-3 ) (1^2) = (3.16 x 10^-8) (r^2)

r = 177.8 m .......Ans

3. now SL need = 60 + 5 = 65 dB

65 = 10 log( I / 10^-12)

I = 3.16 x 10^-6 W/m^2

4. (1 x 10^-3) (1^2) = (3.16 x 10^-6) (r^2)

r = 17.8 m

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