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the howler monkey is the loudest land animal and can be heard up to a distance o

ID: 2157676 • Letter: T

Question

the howler monkey is the loudest land animal and can be heard up to a distance of 6.7 km. Assume the acoustic output of a howler to be uniform in all directions. The distance at which the intensity level of a howler's call is 52dB, in SI units, is closest to: correct answer 17 please show a step by step process. how you get each value that u are putting in the equations. I saw other similar examples and they dont show enough of the process and some of them are wrong. I'm left with an equation 52=20log (6700/r) but i dont understand why they put 20 log instead of 10log, and where does the 6700 comes from, what am i doing wrong. I'm putting in my calculator 20log(6700/52) and i get 42.2 not 16.82... please help ..im desperate :(

Explanation / Answer

see formula is L(dB)=10log(P1/P0)
P1= power at 6.7km=4*3.14*6700^2(since going in all direction,therefore area of sphere)
P0=4*3.14*r^2
52=10log(6700/r)^2
52=20log(6700/r)
2.6=log(6700/r)
10^2.6=6700/r

r=6700/10^2.6=6700/398=17