Rocket travels into space, emits sound - intensity/time question

[fuzzy361]

Rocket travels into space, emits sound -- intensity/time question

Homework Statement

A rocket, starting from rest, travels straight up with an acceleration of 56.7 m/s2. When the rocket is at a height of 722 m, it produces a sound that eventually reaches a ground-based monitoring station directly below. The sound is emitted uniformly in all directions. The monitoring station measures a sound intensity I. Later, the station measures an intensity one-third I. Assuming that the speed of sound is 343 m/s, find the time that has elapsed between the two measurements.

Homework Equations

I= P/A
I=P/(4*pi*r^2)

The Attempt at a Solution

I think I'm completely screwed up in the way I'm viewing this problem (by the way, I'm possibly the worst physics student ever, so please excuse the idiocy of my question). I've been assuming that 722 = r1, so I have to solve for r2 then use that, subtract r1 and use the acceleration and the displacement to find the time elapsed. After looking online and seeing how others attacked this problem, I'm just confused. Could someone explain the actual concept to me?

 

[cepheid]

Figuring out how long it takes for the rocket to get from r1 to r2 only tells you the time between the *emission* of the two sound wavefronts. To get the time between their *reception*, you must also take into account the travel time of the waves.

 

[tiny-tim]

welcome to pf!

hi fuzzy361! welcome to pf!

(try using the X₂ button just above the Reply box )

… I've been assuming that 722 = r1, so I have to solve for r2 then use that, subtract r1 and use the acceleration and the displacement to find the time elapsed.

essentially, that's correct!

use the sound intensity to find r₂

then use the speed of sound to find the time it was at r₂ (obviously, a bit before the sound was actually heard )

then use that time, the acceleration, and the speed at 722 m (which you'll need to calculate first) to find the distance above 722 m

show us what you get

(but i won't see it, I'm off to bed now :zzz:)​