Question

There is evidence that elephants communicate via infrasound, generating rumbling vocalizations as low as 14 Hz that can travel up to 10.0 km. The intensity level of these sounds can reach 103 dB measured at a distance of 5 m from the source. Determine the intensity level of the infrasound 10 km from the source, assuming the sound energy radiates uniformly in all directions.

Answer 1

From the theory we have the equation for the intensityas

I = Pav / 4 ? r^2

where Pav is the average powerradiated by the source

r1 = 5.0 m

r2 = 10 km

= 10^4m

so the intensities of the sound wave radiatingout from the elephant are

I1 = Pav / 4 ?r12 and

I2 = Pav / 4 ?r22

I2 = (r1 /r2)2 I1

we know that

? = 10 log (I / Io)

so the intensity level of the sound at a distancer2 from the elephant is

?2 = 10 log (I2 /Io)

= 10 log[(r1 / r2)2 (I /Io)]

= 10 log(r1 / r2)2 + 10 log (I1/ Io)

= 20 log(r1 / r2) + 10 log (I1 /Io)

= 20 log (5.0m / 10^4m) + ?1

= 20 log (5.0m / 10^4 m) + 103 db

= 36.98 db Answer

I hope help you !!