When the door of the Chapel of the Mausoleum in Hamilton, Scotland, is slammed s

Question

When the door of the Chapel of the Mausoleum in Hamilton, Scotland, is slammed shut, the last echo heard by someone standing just inside the door reportedly comes 28.1 s later.

(a) If that echo were due to a single reflection off a wall opposite the door, how far from the door would that wall be?

I got this as 4.8km and it's a correct answer

(b) If, instead, the wall is 28.8 m away, how many reflections (back and forth, ie if it traveled to the wall and back twice this would count as 3 reflections) correspond to the last echo? Assume the speed of sound is 344 m/s

how do i solve b ??

Explanation / Answer

given that :

the last echo heard by someone standing just inside the door reportedly comes, t = 28.1 sec

(a) If that echo were due to a single reflection off a wall opposite the door, then distance travelled from the door to wall is given as :;

D = v thalf                                 { eq. 1 }

where, v = speed of the sound = 343 m/s

time taken in this case is half of 28.1 sec, since the sound has travel to the wall and back, thalf = 14.05 sec

inserting the values in above eq.

D = (343 m/s) (14.05 sec)

D = 4819.1m

or D = 4.81 km

(b) the back and forth distance is given as :

D' = 2 x 28.8 m = 57.6 m

If, instead, the wall is 28.8 m away, then number of reflections correspond to the last echo which is given as :

N = D / D'                               { eq.2 }

inserting the valuesin eq.2,

N = (4.81km) / (57.6 m)

N = (4.81 x 1000 m) / (57.6 m)

N = 83.5

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